10 little logic puzzles to solve as a family
No screen, no equipment: just a table, a pencil and a wish to work things out together. Here are ten puzzles, from easy to fiendish, three of which use AND, OR and NOT gates. The answers are at the end.
How to play
Read a puzzle aloud, give everyone a minute to think in silence, then pool your ideas. The youngest speaks first; otherwise the same people always answer. Puzzles 1 to 4 suit children from 7 or 8; the last ones need patience, even from adults.
Three puzzles use the logic gates AND, OR and NOT. If those words mean nothing to you, our article for children explains them in five minutes; but common sense works too.
The ten puzzles
- Five daughters (easy). Leah's father has five daughters: Lala, Lele, Lili and Lolo. What is the fifth one called?
- The race (easy). During a race, you overtake the person in second place. What position are you in now?
- The doorbell, an OR gate (easy). The doorbell rings if someone presses the front button OR the back button. Two cousins arrive at the same time, one at each door, and press together. Does it ring?
- Grandma's cake, an AND gate (easy). Grandma gives a slice of cake to anyone who has finished their homework AND hung up their coat. Paul has hung up his coat but not finished his homework. Ines has done both. Milo has done neither. Who gets cake?
- Socks in the dark (medium). A drawer holds 10 red socks and 10 blue socks, all mixed up, and it is pitch dark. What is the smallest number of socks you must take to be sure of having two of the same colour?
- Ages (medium). Today, Emma is three times as old as her little brother. In four years' time, she will be twice his age. How old are they?
- The last biscuit (medium). The last biscuit has vanished. Alice says: “It was Ben.” Ben says: “It wasn't me.” Chloe says: “It wasn't me.” Only one of the three is telling the truth. Who ate the biscuit?
- The wolf, the goat and the cabbage (hard). A ferryman has to take a wolf, a goat and a cabbage across a river. His boat holds only him and one passenger. Left alone with the goat, the wolf eats it; left alone with the cabbage, the goat eats it. How does he do it?
- The lamp with three switches, AND, OR and NOT gates (hard). A lamp lights up when (A OR B) AND NOT C. A, B and C are three switches, up (1) or down (0). Out of the eight possible positions, how many light the lamp, and which?
- The padlock (very hard). A padlock has a three-digit code. Five clues: with 682, one digit is right and in the right place; with 614, one digit is right but in the wrong place; with 206, two digits are right but in the wrong places; with 738, nothing is right; with 780, one digit is right but in the wrong place. What is the code?
Before you look at the answers
When a puzzle won't budge, change your method rather than pushing harder. For the biscuit, try each suspect in turn and count who is telling the truth. For the lamp, write out all eight rows, from 000 to 111: that is a truth table, and it never forgets a case. For the padlock, start with the clue that rules out the most: 738, where nothing is right.
The answers
- Leah: the sentence begins with “Leah's father”.
- Second. You take the place of the person you overtake; to be first, you would have to overtake the leader.
- Yes. An OR gate gives 1 as soon as one input is 1, and also when both are.
- Only Ines. With AND, meeting one condition is not enough.
- Three. With two, you might get one red and one blue; the third must match one of them.
- Emma is 12 and her brother is 4. In four years' time: 16 and 8, twice as old.
- Chloe. If it were Ben, Alice and Chloe would be telling the truth; if it were Alice, Ben and Chloe would. If it is Chloe, only Ben is telling the truth.
- The goat goes first. The ferryman comes back alone, takes the wolf over and brings the goat back. He takes the cabbage over, comes back alone, then takes the goat across: seven crossings in all.
- Three: A up on its own, B up on its own, or A and B both up, always with C down. As soon as C is up, NOT C is 0 and the AND gate switches everything off.
- 042. The 738 clue rules out 7, 3 and 8. The 780 clue says 0 is in the code, but not on the right; the 206 clue says it is not in the middle, so it is on the left. The 6 can no longer be in the right place on the left, so in 682 it is the 2 that is right and in place, on the right. In the middle, the 1 from 614 would be in the right place, so it must be the 4.
We checked every answer with a small program: for the padlock, it tried all 1,000 codes, and only 042 fits the five clues.
Want more? Our truth table page has a three-input circuit to play, very close to puzzle 9.