RIDDLES

I am an odd number.

Take away one letter from me and I become even.

What number am I?

3 cats catch 3 mice in 3 minutes. How long for 100 cats to catch 100 mice?

Father is 40, son is 10. When will father be twice son’s age?

2, 3, 5, 7, 11, 13… What comes next?

You have 10 apples. Give 3 to one friend, 3 to another. How many do you have?

Multiply me by any number, I stay the same.

30 students: half boys, half not boys. How?

What time is it 3 hours after 12?

How can 11 + 6 = 5 ?

Three switches outside, three bulbs inside; enter once. How identify which switch → which bulb?

Speeds 1,2,7,10; one torch; min total?

Twelve coins, one odd (heavy/light). With three balance weighings, identify it and if heavy or light.

8×8 board minus two opposite corners — tile with dominoes?

Pile 21, remove 1/3/4 per turn, who wins and how?

Two nonuniform ropes burn 1 hour each. Get 45 minutes.

2,3,5,9,17,… next?

Switches toggle subsets of bulbs (mod 2). How solve for switches to turn all off?

Four cups: three safe, one poisoned. You may test only once using indicator paper that turns blue if poison is present. How test all four with one test?

You have 2 identical eggs and a 100-floor building. Eggs break at or above a certain floor. Find the breakpoint in the fewest worst-case drops.

A single room has a lightbulb. Prisoners enter one by one. They must determine when everyone has visited the room at least once. What’s the key strategy?

Two integers >1. S knows their sum; P knows their product. After conversation, both know the numbers. What property must the numbers satisfy?

You have 7-L and 5-L jugs. Measure exactly 1 L.

Can a knight visit every square of a standard 8×8 board exactly once and return to start?

Start with any positive integer. Replace it with the product of its non-zero digits. Repeat. What numbers are fixed points?

A corridor has doors numbered 1 to ∞. All start closed. Pass 1 toggles all; pass 2 toggles multiples of 2; pass 3 toggles multiples of 3… After infinite passes, which doors are open?

In a directed acyclic graph with weights, what is the fastest way to compute shortest path from start to end?

Two envelopes; one has twice the money of the other. You pick one but can switch. Should you switch?

Can any planar map be coloured with at most 4 colours so no adjacent regions match?