Start by listing the possibilities. A useful logical argument shows not only why one answer works but also why the other answers fail.
How it works: Read the problem, open a hint only if you need one, then reveal the answer when you're ready.
LogicMedium
The three drawers
Drawers A, B and C each have a label. A says “The key is in B.” B says “The key is not in B.” C says “The key is not in A.” Exactly one statement is true. Where is the key?
First hint
Check whether the key could be in B.
Second hint
For B, the first and third labels would both be true.
Reveal answer and explanation
Drawer AWith the key in A, only the label on drawer B is true. B or C would make two labels true.
LogicMedium
The queue of four
Four friends—Ada, Ben, Cara and Drew—stand in a line. Ben is immediately before Cara. Ada is not at either end. Drew is somewhere after Cara. What is the order?
First hint
Place Ben and Cara together.
Second hint
Drew must be after both Ben and Cara.
Reveal answer and explanation
Ben, Cara, Ada, DrewOnly that arrangement keeps Ben directly in front of Cara, puts Ada in a middle position, and places Drew after Cara.
LogicMedium
Nine coins
Nine identical-looking coins include one heavier coin. You have a balance scale and only two weighings. How do you find the heavy one?
First hint
Divide the coins into three groups.
Second hint
Weigh three against three, then one against one.
Reveal answer and explanation
Weigh 3 vs 3, then 1 vs 1If the first weighing balances, the heavier coin is among the unweighed three; otherwise it is in the heavier group. Compare one coin with another from that group. If they balance, the third is heavier.
LogicEasy
The four crates
Three crates are labelled: A says “The prize is in A”; B says “The prize is in A”; C says “The prize is in B”. Exactly one label is correct. Which crate contains the prize?
First hint
The first two labels claim the same thing.
Second hint
If the prize were in A, how many labels would be correct?
Reveal answer and explanation
Crate BA prize in A would make two labels true; a prize in C would make none true. A prize in B makes only C’s label true.
LogicHard
Bridge at night
Four people take 1, 2, 7 and 10 minutes to cross a bridge. Only two may cross at once; they need a torch, and a pair moves at the slower person’s pace. What is the shortest total time?
First hint
The two fastest people can shuttle the torch.
Second hint
Try sending the two slowest across together.
Reveal answer and explanation
17 minutes1 and 2 cross (2); 1 returns (1); 7 and 10 cross (10); 2 returns (2); 1 and 2 cross (2): total 17 minutes.
LogicHard
The secret code card
Four cards show A, D, 4 and 7. Every card has a letter on one face and a number on the other. To test “If there is a vowel on one side, there is an even number on the other,” which cards must you turn?
First hint
Look for a possible counterexample.
Second hint
An odd number with a vowel on its back would disprove the claim.
Reveal answer and explanation
A and 7Turn A to check that it has an even number, and 7 to check that it does not have a vowel. The other cards cannot disprove the rule.
LogicHard
The two guards
One of two guards always tells the truth; the other always lies. Each guards one of two doors, only one of which is safe. You may ask one yes/no question. What can you ask?
First hint
Make each guard account for the other guard.
Second hint
Ask what the other guard would say about one specific door.
Reveal answer and explanation
Ask “Would the other guard say this door is safe?” and do the oppositeThe truthful guard reports the liar’s false answer. The lying guard lies about the truthful guard’s answer. Either way, the reply points away from the safe door.
LogicMedium
The odd switch
There are three switches outside a closed room and one ordinary filament bulb inside. Exactly one switch operates it. You may enter the room once. How do you identify the correct switch?
First hint
A bulb can reveal more than whether it is on.
Second hint
Turn one switch on for a while, then off; turn a different switch on.
Reveal answer and explanation
Use light and warmthAfter switching the first off and second on, enter. A lit bulb means switch two; an unlit warm bulb means switch one; an unlit cold bulb means switch three. This relies on a bulb that noticeably warms up.
LogicEasy
The only order
Four runners finish a race. Ava finished before Ben. Ben finished before Cy. Dee finished after Cy. What was the finishing order?
First hint
Build a chain from “before”.
Second hint
All three clues connect the same four people.
Reveal answer and explanation
Ava, Ben, Cy, DeeThe clues give Ava before Ben before Cy before Dee, leaving only one possible order.
LogicHard
The burning ropes
Two uneven ropes each take exactly 60 minutes to burn from one end to the other, but burn at irregular rates. With matches and no clock, how could you time exactly 45 minutes?
First hint
Burning a rope from both ends takes 30 minutes.
Second hint
Light one rope at both ends and the other at one end.
Reveal answer and explanation
Light three rope ends, then the fourthStart rope A at both ends and rope B at one end. When A finishes after 30 minutes, light the other end of B; its remaining burn time halves from 30 to 15 minutes. Total: 45 minutes.
