These are the classics — the lockers, the bridge crossing, the mislabelled boxes, the two ropes. Most have been circulating for decades and several have a single elegant solution that is hard to find and obvious afterwards.
That gap between hard-to-find and obvious-afterwards is what makes them last. The answer is not obscure; it is one reframing away. Once you see that the locker toggling is really a question about counting factors, the problem collapses.
Every question below shows all four options, the keyed answer, and the one-line explanation. If you want to turn these into video, the OmniFrame Quiz Studio is free and this pack is built in.
Question 1
You have 100 lockers and toggle every nth locker on pass n. Which lockers stay open?
Why: Only numbers with an odd number of factors remain open, and those are squares.
Question 2
Three people wear two black hats and one white hat. You see two black hats. What color is yours?
Why: If the other two hats are black and only one white hat exists, yours must be white.
Question 3
You can ask one yes/no question to find whether a machine always lies or tells truth. What do you ask?
Why: A known truth calibrates the machine.
Question 4
Four people cross a bridge in 1, 2, 7, and 10 minutes with one flashlight. What is the minimum total?
Why: Send 1 and 2, return 1, send 7 and 10, return 2, then send 1 and 2: 17 minutes.
Question 5
Nine coins include one lighter fake. With two balance weighings, what should the first weighing compare?
Why: A 3-versus-3 weighing identifies which group of three contains the lighter coin; the second finds it.
Question 6
Three switches control three bulbs in another room. What do you use besides sight?
Why: Turn one switch on long enough to warm its bulb, then compare heat and light.
Question 7
You have two ropes that each burn in one hour unevenly. How can you time 45 minutes?
Why: The first rope ends at 30 minutes, then burn the other end of the second rope for 15 more.
Question 8
Twelve coins, one fake that may be heavy or light. What is the fewest balance weighings that always finds it?
Why: Three weighings distinguish 27 outcomes, enough to cover 24 possible coin-and-direction cases.
Question 9
Ask either guard which door the other would call safe. What should you do with the door they indicate?
Why: The liar and truth-teller both indicate the unsafe door when asked what the other would say.
Question 10
In the wolf, goat, and cabbage crossing, which passenger must cross first?
Why: The goat cannot be left with wolf or cabbage without the farmer.
Question 11
What comes next: 1, 1, 2, 3, 5, 8?
Why: Each number is the sum of the previous two.
Question 12
Three boxes are labeled Apples, Oranges, and Mixed, but every label is wrong. Which box should you sample?
Why: Because every label is wrong, the Mixed-labeled box contains one fruit type; one sample lets you relabel all three.
Question 13
You need exactly 4 liters using 3 and 5 liter jugs. What do you do?
Why: Emptying the 3-litre jug first leaves room for the 2 litres, so topping it up later draws exactly 1 from the full 5.
Question 14
Two fathers and two sons catch three fish, and each gets one. How many people are there?
Why: They are a grandfather, his son, and his grandson: two fathers and two sons among three people.
Question 15
What number is missing: 2, 6, 12, 20, 30, ?
Why: The pattern is n times n+1: 1x2, 2x3, 3x4, and so on.
These questions are free to use — in a classroom, a pub quiz, a video, or anywhere else. No attribution required. If you think one is ambiguous or an explanation is wrong, tell us and we will fix the page.
For how questions like these are constructed, see what makes a quiz question hard.