90 logic puzzles with worked solutions

Read the clues, give the group time to reason, then open the worked solution to check the route as well as the answer.

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Esme, Hana, Jada and Nia each borrowed a library book: the bird book, the river book, the robot book or the volcano book, one each. Nia does not have the bird book. Jada does not have the robot book. The volcano book belongs to either Esme or Hana. The bird book belongs to either Hana or Nia. Who has which book?

Logic puzzles for kids with answers

24 puzzles

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Logic puzzles for kids with answers 24 puzzles
Four friends, four things, one each. Cross off what the clues rule out until only one match is left in every row, then check the worked answer.
Sudoku puzzles with answers 18 puzzles
Fill every row, column and 3 × 3 box with the numbers 1 to 9. Solve on screen, or print the puzzles and the answer key; the hint names the first square you can fill.
Sudoku for kids with answers 12 puzzles
Small grids for young solvers: fill every row, column and box with 1 to 4, or with 1 to 6. Stuck on a 6 × 6? Write the numbers a square could still take small in its corner, and cross them off as you fill the rest. Solve on screen or print them with the answers.
Jigsaw sudoku with answers 12 puzzles
The 3 × 3 boxes are gone: each grid is cut into nine outlined pieces of nine squares, and every row, column and piece holds 1 to 9 once. Solve on screen or print them with the answers.
Killer sudoku with answers 12 puzzles
No numbers are given. Each dashed cage shows the total of its squares, and no number repeats inside a cage. Begin with the cages that can be made only one way. Solve on screen or print them with the answers.
Word sudoku with answers 9 puzzles
Sudoku with letters: each grid uses the letters of one word, once in every row, column and box, and when it is solved one row spells the word. Nine-letter grids, then six-letter grids for younger solvers. Solve on screen or print them.
Samurai sudoku with answers 6 puzzles
Five sudoku grids that overlap: the middle grid shares each corner box with an outer grid, so a number placed in one helps solve the next. Every row, column and box of each grid holds 1 to 9 once. Solve on screen, one grid at a time on a phone, or print them with the answers.
Magic squares with answers 12 puzzles
Write the numbers in the grid so that every row, every column and both diagonals add to the same total. Start on 3 × 3 squares of 1 to 9, then other numbers, then 4 × 4. Solve on screen with running totals, or print them with the answers.
Kakuro puzzles with answers 12 puzzles
A crossword of numbers: write 1 to 9 in the white squares so each run adds to the total in the grey square before it, with no number repeated in a run. Easy grids first, then bigger ones. Solve on screen, where each square shows the ways its runs can be made, or print them with the answers.
Number search puzzles with answers 12 puzzles
A word search written in digits: find each number in the list hidden in the grid. Easy grids run across and down, harder ones diagonally and backwards. Every number appears exactly once. Solve on screen or print them with the answer key.
Number fill-in puzzles with answers 12 puzzles
A crossword with numbers and no clues: fit every number in the list into the grid, across or down, one digit a square. One number is written in to start. Solve on screen, where each number crosses itself off once it is placed, or print them with the answers.
Logic grid puzzles with solutions 18 puzzles
Match each person to one item. Each match can be used only once; the solutions explain each deduction.
Logic puzzles online with working grids
Mark each pairing as unknown, impossible or confirmed. Check your solution when every row has a confirmed match.
Daily logic puzzle with a worked solution
A new puzzle for each date: a logic grid, a truth-teller puzzle or a number puzzle in turn. Reveal the reasoning or print it with the answer.
Printable logic grid paper
Print the finished sheet or download its PDF. Use the rules below to set up the game.
Printable blank sudoku grids
Choose a grid size, then print or download the blank worksheet. Copy your own puzzle into the grid.
Number puzzles with answers

90 puzzles · Logic puzzles with worked solutions · answers included

Updated 3 Nov 2026

Grid deduction

1
Ivo, Lea, and Mina present at 9, 10, and 11, one person per time. Ivo presents at 9. Lea is not at 9. Mina is not at 10. Who presents at 10?

Solve it on screen

Answer
Lea presents at 10.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Ivo uses 9. Mina cannot use 9 or 10, so Mina uses 11. The remaining time, 10, belongs to Lea.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
2
Ari, Bo, Cia, and Dev each choose one project: kite, maze, robot, or volcano. Ari chooses neither maze, robot, nor volcano. Bo chooses neither robot nor volcano. Cia does not choose volcano. Which project does Dev choose?

Solve it on screen

Answer
Dev chooses the volcano project.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Ari must have kite. Bo then must have maze. Cia must have robot, leaving volcano for Dev.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
3
Four workshops use Cedar, Elm, Maple, and Oak rooms. Design is not in Elm, Maple, or Oak. Coding is not in Cedar, Maple, or Oak. Writing is not in Cedar, Elm, or Oak. Where is the Music workshop?

Solve it on screen

Answer
Music is in Oak.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Design is forced into Cedar, Coding into Elm, and Writing into Maple. Oak is the only room left for Music.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
4
Four labeled lunch boxes contain apple, crackers, grapes, and yogurt, one snack each. Box Red has crackers. Box Blue has neither apple nor yogurt. Box Green has neither crackers nor yogurt. What is in Box Yellow?

Solve it on screen

Answer
Box Yellow contains yogurt.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Red has crackers. Blue cannot have apple or yogurt, so Blue has grapes. Green then has apple. Yogurt remains for Yellow.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
5
Jae, Kira, Luis, and Noor each visit on Monday, Tuesday, Wednesday, or Thursday. Noor visits Thursday. Jae does not visit Tuesday or Wednesday. Kira does not visit Monday or Wednesday. Which day does Luis visit?

Solve it on screen

Answer
Luis visits Wednesday.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Noor has Thursday. Jae must have Monday. Kira must then have Tuesday. Wednesday remains for Luis.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
6
Eli, Fara, Gus, Hana, and Ivan wear circle, diamond, moon, square, and star badges. Eli does not wear diamond, moon, square, or star. Fara does not wear moon, square, or star. Gus does not wear square or star. Hana does not wear star. Which badge does Ivan wear?

Solve it on screen

Answer
Ivan wears the star badge.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
The exclusions force Eli to circle, Fara to diamond, Gus to moon, and Hana to square. Star remains for Ivan.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
7
Paz, Quin, Ravi, and Sol use lockers 12, 18, 24, and 30. Ravi uses 24. Paz does not use 18 or 30. Quin does not use 12 or 30. Which locker does Sol use?

Solve it on screen

Answer
Sol uses locker 30.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Ravi has 24. Paz must have 12. Quin must have 18. Sol therefore has 30.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
8
Uma, Vero, Wes, and Xia play drum, flute, piano, and violin. Xia plays violin. Uma plays neither flute nor piano. Vero plays neither drum nor piano. Which instrument does Wes play?

Solve it on screen

Answer
Wes plays piano.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Xia has violin. Uma must have drum, and Vero must have flute. Piano remains for Wes.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
9
Packets A, B, C, and D contain basil, dill, mint, and thyme. Packet B contains dill. Packet A contains neither dill nor mint nor thyme. Packet C contains neither basil, dill, nor thyme. What is in Packet D?

Solve it on screen

Answer
Packet D contains thyme.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
A must contain basil and B contains dill. C cannot contain basil, dill, or thyme, so C has mint. The remaining herb, thyme, belongs in D.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
10
Four parcels arrive by bike, car, train, and van. Parcel North arrives by train. Parcel East arrives by neither car nor van. Parcel South arrives by neither bike nor van. How does Parcel West arrive?

Solve it on screen

Answer
Parcel West arrives by van.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
North uses train. East must use bike. South must use car. Van remains for West.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
11
Clay, glass, paper, and wood models sit on shelves 1, 2, 3, and 4. Glass is on shelf 2. Clay is not on shelves 2, 3, or 4. Paper is not on shelves 1, 2, or 4. Which shelf holds wood?

Solve it on screen

Answer
Wood is on shelf 4.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Clay is forced to shelf 1, glass is on shelf 2, and paper is forced to shelf 3. Wood must be on shelf 4.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
12
Nia, Oren, and Pia each use a telescope at dawn, noon, or dusk. Oren uses it at noon. Nia uses it at neither noon nor dusk. When does Pia use it?

Solve it on screen

Answer
Pia uses the telescope at dusk.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Oren takes noon. Nia can take neither noon nor dusk, so Nia takes dawn. The remaining slot, dusk, belongs to Pia.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
13
Red, Blue, Green, and White recipe cards show soup, rice, salad, and stew. White shows stew. Red shows neither rice, salad, nor stew. Blue shows neither soup, salad, nor stew. What does Green show?

Solve it on screen

Answer
Green shows salad.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
White has stew. Red is excluded from the other three choices, so Red has soup. Blue must then have rice, leaving salad for Green.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
14
Kite, Lime, Moss, and Navy envelopes contain a badge, map, pass, and token. Moss contains the pass. Kite contains neither the map, pass, nor token. Lime contains neither the badge, pass, nor token. What is in Navy?

Solve it on screen

Answer
Navy contains the token.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Moss has the pass. Kite is forced to the badge and Lime is forced to the map. The only insert left for Navy is the token.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
15
Aster, Birch, Cedar, Dune, and Elm segments occupy radio slots 1 through 5. Aster has slot 3. Birch has none of slots 2 through 5. Cedar has neither slot 1 nor slots 3 through 5. Dune has neither slots 1 through 3 nor slot 5. Which slot has Elm?

Solve it on screen

Answer
Elm has slot 5.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Aster has 3. The exclusions force Birch to 1, Cedar to 2, and Dune to 4. Slot 5 remains for Elm.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
16
Five lanterns named Arc, Beam, Cove, Drift, and Echo glow amber, blue, green, silver, and violet. Cove glows green. Arc glows neither blue, green, silver, nor violet. Beam glows neither amber, green, silver, nor violet. Drift glows neither amber, blue, green, nor violet. What color is Echo?

Solve it on screen

Answer
Echo glows violet.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Cove has green. Arc is forced to amber, Beam to blue, and Drift to silver. Violet is the remaining color for Echo.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
17
Poster tubes J, K, L, M, and N hold art, code, dance, music, and science posters. Tube L holds dance. Tube J holds neither code, dance, music, nor science. Tube K holds neither art, dance, music, nor science. Tube M holds neither art, code, dance, nor science. Which poster is in Tube N?

Solve it on screen

Answer
Tube N holds the science poster.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
Tube L has dance. The exclusions force J to art, K to code, and M to music. Science remains for Tube N.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
18
Folders A through F have coral, gold, gray, lilac, teal, and white tabs. Folder C has gray. A has none of gold, gray, lilac, teal, or white. B has none of coral, gray, lilac, teal, or white. D has none of coral, gold, gray, teal, or white. E has none of coral, gold, gray, lilac, or white. Which tab does F have?

Solve it on screen

Answer
Folder F has the white tab.
In the grid, bold crosses come straight from the clues, thin crosses follow once a row or column has its tick, and each circled tick is a match.
C has gray. The exclusions force A to coral, B to gold, D to lilac, and E to teal. White remains for F.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes

Sequence rules

19
Start at 4 and add 7 each time: 4, 11, 18, 25, 32. What is the next term?

Answer
39.
Add 7 to 32. The result is 39.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
20
Start at 2 and multiply by 3 each time: 2, 6, 18, 54. What is the next term?

Answer
162.
Multiply 54 by 3. The result is 162.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
21
Starting at 4, alternate add 3 and multiply by 2: 4, 7, 14, 17, 34. What is next?

Answer
37.
The last operation shown was multiply by 2, so the next operation is add 3. Then 34 + 3 = 37.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
22
Start at 3 and add consecutive even numbers 2, 4, 6, 8, and so on: 3, 5, 9, 15, 23, 33. What is next?

Answer
45.
The next even-number gap is 12, so 33 + 12 = 45.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
23
The nth term is n times n + 1, beginning with n = 1: 2, 6, 12, 20, 30. What is the sixth term?

Answer
42.
For n = 6, calculate 6 times 7, which is 42.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
24
Begin with 2 and 3, then make each new term the sum of the previous two: 2, 3, 5, 8, 13, 21. What is next?

Answer
34.
Add the previous two terms: 13 + 21 = 34.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
25
The odd-position terms start at 2 and rise by 4. The even-position terms start at 20 and fall by 3: 2, 20, 6, 17, 10, 14, 14, 11. What is next?

Answer
18.
The next term is in an odd position. Continue 2, 6, 10, 14 by adding 4 to get 18.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
26
Start at 3. Double each term and subtract 1: 3, 5, 9, 17, 33. What is next?

Answer
65.
Double 33 to get 66, then subtract 1 to get 65.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
27
Starting at 10, add 5, subtract 2, add 10, subtract 4, add 15, and continue the two growing patterns: 10, 15, 13, 23, 19, 34. What is next?

Answer
28.
The subtraction amounts are 2, 4, then 6. Subtract 6 from 34 to get 28.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0
28
The nth term is n cubed minus 1, beginning with n = 1: 0, 7, 26, 63, 124. What is the sixth term?

Answer
215.
Six cubed is 216. Subtract 1 to get 215.
Source: Method source https://nrich.maths.org/patterns-and-sequences-short-problems-0

Balance-scale deductions

29
Coins A, B, and C contain exactly one heavier coin. A balances B. Which coin is heavier?

Answer
Coin C.
A and B have equal weight, so neither can be the one heavier coin. C is the only candidate left.
Source: Method source https://nrich.maths.org/problems/weighing-scales
30
Among A, B, C, and D, exactly one item is lighter. A and B outweigh C and D. Then C outweighs D. Which item is lighter?

Answer
D is lighter.
The first weighing places the lighter item among C and D. Since C outweighs D, D is the lighter item.
Source: Method source https://nrich.maths.org/problems/weighing-scales
31
Five items A through E include exactly one heavier item. A and B balance C and D. Which item is heavier?

Answer
E is heavier.
All four weighed items balance in equal-size groups, so none is heavier. The unweighed item E must be heavier.
Source: Method source https://nrich.maths.org/problems/weighing-scales
32
Six items A through F include exactly one lighter item. A, B, and C are lighter as a group than D, E, and F. Then A outweighs B. Which item is lighter?

Answer
B is lighter.
The first result puts the lighter item among A, B, and C. A outweighs B, so B is lighter than A. If C were lighter, A and B would balance. Therefore B is the odd item.
Source: Method source https://nrich.maths.org/problems/weighing-scales
33
Seven items A through G include exactly one heavier item. A, B, and C balance D, E, and F. Which item is heavier?

Answer
G is heavier.
The six weighed items balance, so the only unweighed candidate G is heavier.
Source: Method source https://nrich.maths.org/problems/weighing-scales
34
Eight labeled items A through H include exactly one heavier item. A, B, and C are lighter as a group than D, E, and F. D balances E. Which item is heavier?

Answer
F is heavier.
The first result puts the heavier item among D, E, and F. D balances E, so F is the only candidate.
Source: Method source https://nrich.maths.org/problems/weighing-scales
35
One item among A through H is lighter than all the others. A, B, and C are lighter as a group than D, E, and F. A balances B. Which item is lighter?

Answer
C is lighter.
The first result puts the lighter item among A, B, and C. A balances B, leaving C.
Source: Method source https://nrich.maths.org/problems/weighing-scales
36
Of the nine items A through I, exactly one is heavier. A, B, and C balance D, E, and F. Then G is lighter than H. Which item is heavier?

Answer
H is heavier.
The first balance puts the heavier item among G, H, and I. H outweighs G. If I were heavier, G and H would balance. Therefore H is heavier.
Source: Method source https://nrich.maths.org/problems/weighing-scales
37
Within items A through J, exactly one is lighter. A, B, and C balance D, E, and F. G and H outweigh I and J. Then I outweighs J. Which item is lighter?

Answer
J is lighter.
The first balance leaves G, H, I, and J. The second result places the lighter item among I and J. Since I outweighs J, J is lighter.
Source: Method source https://nrich.maths.org/problems/weighing-scales
38
Twelve items labeled A through L include exactly one heavier item. A through D balance E through H. I and J are lighter as a pair than K and L. K outweighs L. Which item is heavier?

Answer
K is heavier.
The first balance leaves I, J, K, and L. The second result puts the heavier item among K and L. The final weighing identifies K.
Source: Method source https://nrich.maths.org/problems/weighing-scales
39
Exactly one of four tiles A, B, C, and D is heavier. A balances B, then C outweighs A. Which tile is heavier?

Answer
C is heavier.
The balance removes A and B from consideration. C outweighs a known normal tile, so C is the unique heavier tile and D is normal.
Source: Method source https://nrich.maths.org/problems/weighing-scales
40
Five counters A through E contain exactly one lighter counter. A and B balance C and D. Which counter is lighter?

Answer
E is lighter.
A balanced comparison shows A, B, C, and D all have normal weight. E is the only counter not cleared, so E must be lighter.
Source: Method source https://nrich.maths.org/problems/weighing-scales
41
Among six blocks A through F, one is heavier. A and B balance C and D. A second weighing shows E outweighs A. Which block is heavier?

Answer
E is heavier.
The first balance clears A through D, leaving E or F. Since E outweighs the known normal block A, E is the heavier block.
Source: Method source https://nrich.maths.org/problems/weighing-scales
42
Seven discs A through G include one lighter disc. A, B, and C balance D, E, and F. Identify the lighter disc.

Answer
G is lighter.
The six weighed discs balance, so none of them is the lighter one. G is the only unweighed disc and must be lighter.
Source: Method source https://nrich.maths.org/problems/weighing-scales
43
A set of nine tokens A through I has one lighter token. A through D balance E through H. Which token is lighter?

Answer
I is lighter.
The eight tokens on the balanced pans all have normal weight. I is the only token outside that cleared set, so I is lighter.
Source: Method source https://nrich.maths.org/problems/weighing-scales
44
Ten beads A through J include one heavier bead. A through D balance E through H. Then J outweighs I. Which bead is heavier?

Answer
J is heavier.
The first balance clears A through H and leaves only I or J. J outweighs I, so J is the heavier bead.
Source: Method source https://nrich.maths.org/problems/weighing-scales
45
Eleven cubes A through K include one heavier cube. A through D balance E through H, and I balances J. Which cube is heavier?

Answer
K is heavier.
The first balance clears A through H. The second balance clears I and J. K is the only cube not shown to be normal, so K is heavier.
Source: Method source https://nrich.maths.org/problems/weighing-scales

River crossings

46
One adult weighs 2 units and two children weigh 1 unit each. A boat holds 2 units, everyone can row, and nobody may swim. What is the minimum number of one-way crossings?

Answer
5 crossings.
Children 1 and 2 cross; Child 1 returns; Adult crosses; Child 2 returns; both children cross. That is five crossings.
Source: Method source https://nrich.maths.org/problems/river-crossing
47
Two adults weigh 2 units each and two children weigh 1 unit each. A boat holds 2 units, everyone can row, and nobody may swim. What is the minimum number of one-way crossings?

Answer
9 crossings.
Both children cross; one returns; Adult 1 crosses; the other child returns; both children cross; one returns; Adult 2 crosses; the other child returns; both children cross. Nine crossings are necessary.
Source: Method source https://nrich.maths.org/problems/river-crossing
48
Three adults weigh 2 units each and two children weigh 1 unit each. A boat holds 2 units, everyone can row, and nobody may swim. What is the minimum number of one-way crossings?

Answer
13 crossings.
Use four crossings to transfer one adult while resetting both children to the starting bank. Repeat for each adult, then send both children across. The total is 4 + 4 + 4 + 1 = 13.
Source: Method source https://nrich.maths.org/problems/river-crossing
49
Ari, Bo, and Cy weigh 1, 2, and 3 units. The boat holds 3 units and all three can row. What is the minimum number of one-way crossings?

Answer
5 crossings.
Ari and Bo cross; Ari returns; Cy crosses; Bo returns; Ari and Bo cross. The total is five.
Source: Method source https://nrich.maths.org/problems/river-crossing
50
Dax, Emi, Flo, and Gio weigh 1, 2, 3, and 4 units. The boat holds 5 units and all four can row. What is the minimum number of one-way crossings?

Answer
5 crossings.
Dax and Gio cross; Dax returns; Emi and Flo cross; Emi returns; Dax and Emi cross. The total is five.
Source: Method source https://nrich.maths.org/problems/river-crossing
51
A guide must take a fox, a hen, and grain across. The boat carries the guide plus one item. Without the guide, the fox cannot stay with the hen, and the hen cannot stay with the grain. What is the minimum number of one-way crossings?

Answer
7 crossings.
Take hen over; return alone; take fox over; bring hen back; take grain over; return alone; take hen over. Seven is the shortest safe route.
Source: Method source https://nrich.maths.org/problems/river-crossing
52
A guide must move A, B, C, and D across in a boat holding two items. When unattended, A cannot stay with B, B cannot stay with C, and C cannot stay with D. What is the minimum number of one-way crossings?

Answer
3 crossings.
Take A and C over; return alone; take B and D over. Both unattended pairs of items are safe, and all four arrive in three crossings.
Source: Method source https://nrich.maths.org/problems/river-crossing
53
A guide must move cats C1 and C2 plus mice M1 and M2. The boat holds two animals. When unattended, C1 cannot stay with M1 and C2 cannot stay with M2. What is the minimum number of one-way crossings?

Answer
3 crossings.
Take both cats over; return alone; take both mice over. Each unattended bank contains only one animal type, so the route is safe and uses three crossings.
Source: Method source https://nrich.maths.org/problems/river-crossing
54
A guide must move A, B, C, D, and E in a boat holding two items. When unattended, each neighboring letter pair is unsafe: A-B, B-C, C-D, and D-E. What is the minimum number of one-way crossings?

Answer
7 crossings.
A shortest safe route is B and D over; return alone; A over; B back; C and E over; D back; B and D over. This uses seven crossings.
Source: Method source https://nrich.maths.org/problems/river-crossing
55
Ada and Bran each weigh 1 unit, and Ciro weighs 2 units. A boat holds 3 units, everyone can row, and nobody may swim. What is the minimum number of one-way crossings?

Answer
3 crossings.
Ada and Ciro cross, Ada returns, then Ada and Bran cross. All three finish across in three trips, and one trip cannot carry all 4 units.
Source: Method source https://nrich.maths.org/problems/river-crossing
56
Dara and Eli weigh 1 unit each, while Finn and Gail weigh 2 units each. The boat holds 3 units and everyone can row. Find the minimum number of one-way crossings.

Answer
5 crossings.
Dara takes Finn over and returns. Dara takes Gail over and returns again. Dara and Eli then cross together, for five crossings.
Source: Method source https://nrich.maths.org/problems/river-crossing
57
Hugo, Iris, and Juno weigh 1 unit each; Kai and Luz weigh 2 units each. The boat holds 3 units and all five can row. Determine the fewest one-way crossings.

Answer
5 crossings.
Hugo takes Kai over and returns, then takes Luz over and returns. Hugo, Iris, and Juno cross together on the fifth trip.
Source: Method source https://nrich.maths.org/problems/river-crossing
58
Mara weighs 1 unit and can row. Niko and Ola each weigh 2 units and cannot row. A boat holds 3 units. How few one-way crossings move everyone across?

Answer
3 crossings.
Mara rows Niko across, returns alone, and rows Ola across. Both loaded trips meet the 3-unit limit, so three crossings suffice.
Source: Method source https://nrich.maths.org/problems/river-crossing
59
Pax and Quin weigh 1 unit and can row. Rumi and Sela weigh 2 units and cannot row. With a 3-unit boat, what is the minimum number of one-way crossings?

Answer
5 crossings.
Pax rows Rumi across and returns, then rows Sela across and returns. Pax and Quin cross together on trip five.
Source: Method source https://nrich.maths.org/problems/river-crossing
60
Tara and Ugo weigh 1 unit and can row. Vera, Wynn, and Xeno weigh 2 units and cannot row. The boat holds 3 units. What is the minimum crossing count?

Answer
7 crossings.
Tara ferries Vera, Wynn, and Xeno one at a time, returning after the first two. Tara returns once more for Ugo, and the two rowers make the seventh crossing together.
Source: Method source https://nrich.maths.org/problems/river-crossing
61
Yara and Zed weigh 1 unit each, Ami weighs 2 units, and Bex weighs 3 units. A boat holds 4 units and everyone can row. What is the fewest number of one-way crossings?

Answer
3 crossings.
Yara and Bex cross at the 4-unit limit. Yara returns, then crosses with Zed and Ami, again totaling 4 units. Three crossings are enough.
Source: Method source https://nrich.maths.org/problems/river-crossing
62
Cora and Deni weigh 1 unit each, Evan weighs 2, and Faye and Gino weigh 3 each. Everyone can row a boat holding 4 units. Find the minimum one-way crossings.

Answer
5 crossings.
Cora takes Faye across and returns, then takes Gino across and returns. Cora, Deni, and Evan make the fifth trip at the 4-unit limit.
Source: Method source https://nrich.maths.org/problems/river-crossing

Knights and knaves

63
On the island, A says, 'B and I are different types.' B says, 'A is a knave.' Who is who?

Answer
A=knight; B=knave.
If A is truthful, the two differ, so B is a knave and B's claim is false. If A is a knave, the two would be the same, making B a knave whose claim that A is a knave is true, which is impossible.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
64
A says, 'B is a knight.' B says, 'A and I are different types.' Who is who?

Answer
A=knave; B=knave.
If A were a knight, B would be a knight, but then B's different-types claim would be false. Therefore A is a knave, so B is not a knight. Both are knaves, making B's different-types claim false as required.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
65
A says, 'B and I are both knaves.' A is the only speaker. Who is who?

Answer
A=knave; B=knight.
A cannot be a knight while truthfully calling A a knave. So A is a knave and the whole statement is false. With A already a knave, B must be a knight to make 'both knaves' false.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
66
A says, 'A and B are both knaves.' B says, 'C is a knave.' Who is who?

Answer
A=knave; B=knight; C=knave.
A's self-including claim forces A to be a knave and B to be a knight. B then speaks truthfully, so C is a knave.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
67
A says, 'A and B are both knaves.' B says, 'C is a knave.' C says, 'D is a knight.' Who is who?

Answer
A=knave; B=knight; C=knave; D=knave.
The first statement forces A knave and B knight. B truthfully makes C a knave. C's statement must be false, so D is a knave.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
68
A says, 'Exactly one of A and B is a knight.' B says, 'C is a knight.' C says, 'A is a knave.' Who is who?

Answer
A=knight; B=knave; C=knave.
Testing the eight role rows leaves one consistent row: A knight makes the exactly-one claim true; B knave makes 'C is a knight' false; C knave makes 'A is a knave' false.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
69
A says, 'B is a knight or C is a knight.' B says, 'A is a knave.' C says, 'B is a knave.' Who is who?

Answer
A=knight; B=knave; C=knight.
A knight makes the or-claim true through C. B is a knave because its claim about A is false. C is a knight because it truthfully identifies B.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
70
A says, 'B and C are the same type.' B says, 'A is a knight.' C says, 'B is a knave.' Who is who?

Answer
A=knave; B=knave; C=knight.
The consistent row has A knave, so A's same-type claim is false. B is a knave and falsely calls A a knight. C is a knight and truthfully calls B a knave.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
71
A says, 'Exactly one of B and C is a knight.' B says, 'A is a knave.' C says, 'B is a knave.' Who is who?

Answer
A=knight; B=knave; C=knight.
A and C as knights and B as knave makes every statement fit: exactly one of B and C is a knight, B falsely calls A a knave, and C truthfully calls B a knave.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
72
A says, 'Exactly one of B and C is a knave.' B says, 'A is a knight.' C says, 'B is a knave.' D says, 'C is a knave.' Who is who?

Answer
A=knight; B=knight; C=knave; D=knight.
A, B, and D speak truthfully while C lies. Exactly one of B and C is a knave, B correctly identifies A, C falsely identifies B, and D correctly identifies C.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
73
A says, 'It is not true that B and C are both knights.' B says, 'A and C are different types.' C says, 'A is a knight.' Who is who?

Answer
A=knight; B=knave; C=knight.
With A and C knights and B knave, A truthfully denies that B and C are both knights, B falsely says A and C differ, and C truthfully identifies A.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
74
Two islanders speak. A says, 'B is a knave.' B says, 'A and B are different types.' Determine both roles.

Answer
A=knave; B=knight.
If A were a knight, B would be a knave but B's different-types statement would be true. Therefore A is a knave, A's claim is false, and B is a knight.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
75
A says, 'Exactly one of A, B, and C is a knight.' B says, 'A is a knight.' C says, 'B is a knight.' Assign every role.

Answer
A=knave; B=knave; C=knave.
If A were truthful, B and then C would also be knights, contradicting A's count of one. With A a knave, B and C both speak falsely, leaving zero knights and making A's count false.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
76
Three islanders speak. A says, 'B is a knight.' B says, 'C is a knave.' C says, 'A and B are the same type.' Identify A, B, and C.

Answer
A=knave; B=knave; C=knight.
A's statement makes A and B the same type. C therefore tells the truth, so C is a knight. B's claim that C is a knave is false, making B and A knaves.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
77
A says, 'B and C are different types.' B says, 'A is a knave.' C says, 'B is a knight.' Find the three roles.

Answer
A=knave; B=knight; C=knight.
C has the same role as B because C claims B is a knight. A's different-types claim is therefore false, so A is a knave. B then truthfully identifies A.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
78
A says, 'B is a knave.' B says, 'C is a knight.' C says, 'D is a knave.' D says, 'A and C are the same type.' Who is who?

Answer
A=knave; B=knight; C=knight; D=knave.
The first three statements force A opposite B, B equal to C, and C opposite D. Thus A and D match while A and C differ. D's same-type claim is false, fixing D and A as knaves and B and C as knights.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
79
A says, 'Exactly two of A, B, C, and D are knights.' B says, 'A is a knight.' C says, 'B is a knave.' D says, 'C is a knight.' Resolve the roles.

Answer
A=knight; B=knight; C=knave; D=knave.
B must match A, while C and D must both oppose A. Either branch contains two knights, so A's count is true and A must be a knight. The chain then fixes B as knight and C and D as knaves.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes
80
A says, 'Exactly four of A, B, C, D, and E are knights.' B says, 'A is a knight.' C says, 'B is a knight.' D says, 'C is a knave.' E says, 'D is a knight.' Assign all five roles.

Answer
A=knave; B=knave; C=knave; D=knight; E=knight.
B and C match A, while D and E oppose A. This creates either three or two knights, never four, so A's statement is false. A, B, and C are knaves, while D and E are knights.
Source: Method source https://mathigon.org/world/Logic_and_Paradoxes

Cryptarithms

81
Solve SEND + MORE = MONEY. Different letters are different digits, and a leading letter is not zero.

Answer
9567 + 1085 = 10652. S=9, E=5, N=6, D=7, M=1, O=0, R=8, Y=2.
Column-by-column carry constraints and distinct digits leave one mapping: S9 E5 N6 D7 M1 O0 R8 Y2.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
82
Solve I + BB = ILL. Different letters are different digits, and a leading letter is not zero.

Answer
1 + 99 = 100. I=1, B=9, L=0.
The hundreds carry forces I=1. The tens and ones columns then force B=9 and L=0.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
83
Solve CROSS + ROADS = DANGER. Different letters are different digits, and a leading letter is not zero.

Answer
96233 + 62513 = 158746. C=9, R=6, O=2, S=3, A=5, D=1, N=8, G=7, E=4.
Exhaustive column search leaves the mapping C9 R6 O2 S3 A5 D1 N8 G7 E4.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
84
Solve FORTY + TEN + TEN = SIXTY. Different letters are different digits, and a leading letter is not zero.

Answer
29786 + 850 + 850 = 31486. F=2, O=9, R=7, T=8, Y=6, E=5, N=0, S=3, I=1, X=4.
Exhaustive column search leaves F2 O9 R7 T8 Y6 E5 N0 S3 I1 X4.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
85
Solve DONALD + GERALD = ROBERT. Different letters are different digits, and a leading letter is not zero.

Answer
526485 + 197485 = 723970. D=5, O=2, N=6, A=4, L=8, G=1, E=9, R=7, B=3, T=0.
Exhaustive column search leaves D5 O2 N6 A4 L8 G1 E9 R7 B3 T0.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
86
Solve BASE + BALL = GAMES. Different letters are different digits, and a leading letter is not zero.

Answer
7483 + 7455 = 14938. B=7, A=4, S=8, E=3, L=5, G=1, M=9.
Exhaustive column search leaves B7 A4 S8 E3 L5 G1 M9.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
87
Solve EAT + THAT = APPLE. Different letters are different digits, and a leading letter is not zero.

Answer
819 + 9219 = 10038. E=8, A=1, T=9, H=2, P=0, L=3.
Exhaustive column search leaves E8 A1 T9 H2 P0 L3.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
88
Solve COCA + COLA = OASIS. Different letters are different digits, and a leading letter is not zero.

Answer
8186 + 8106 = 16292. C=8, O=1, A=6, L=0, S=2, I=9.
Exhaustive column search leaves C8 O1 A6 L0 S2 I9.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
89
Solve TO + GO = OUT. Different letters are different digits, and a leading letter is not zero.

Answer
21 + 81 = 102. T=2, O=1, G=8, U=0.
Exhaustive column search is used to test whether this proposed mapping is the only valid one.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf
90
Solve NO + NO + TOO = LATE. Different letters are different digits, and a leading letter is not zero.

Answer
74 + 74 + 944 = 1092. N=7, O=4, T=9, L=1, A=0, E=2.
Exhaustive column search is used to test whether this proposed mapping is the only valid one.
Source: Method source https://nrich.maths.org/sites/default/files/thumbnails/content-01-06-six2-Two%252520and%252520Two.pdf

Questions about logic puzzles with worked solutions

How do you solve a logic grid puzzle?

List one group of things across the top of a grid and the other down the side. Put a cross where a clue rules a pairing out and a tick where it confirms one. When a row has one open square left, that is the match.

Can I solve logic puzzles online?

Yes. The online logic grid lets you mark each pairing and checks your grid, and the grid paper page prints blank grids for any puzzle.

Is there a new puzzle every day?

Yes. The daily puzzle page shows a new puzzle for each date, taking turns between a logic grid, a truth-teller puzzle and a number puzzle, and keeps the last 30 days to revisit.

Which puzzles suit children?

The logic puzzles for kids page has short four-person grids, and each answer crosses off the clues step by step.

How to cite this

MadBright, "90 Logic Puzzles With Worked Solutions", https://madbright.com/logic-puzzles, updated 3 Nov 2026.

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