## Nob’s Number Tree Puzzle

Nob’s Number Tree What number belongs in the “?” circle? Note that all numbers shown are correct, there are no typos or errors. Nob Yoshigahara’s Puzzles Nob’s Number Tree is a well-known brainteaser by the Japanese puzzle guru Nobuyuki “Nob”…

## Missing Dollar Riddle

The missing dollar riddle is a classic brain teaser that can trip up even savvy puzzle solvers: Three friends split the cost of a hotel room. They are charged \$30, so each of them pays \$10. Later the hotel manager…

## Divisible by 100

Prove that for any set of one hundred whole numbers, either one of those numbers is divisible by 100 or the sum of a subset of those numbers is divisible by 100.

## Throwing a Ball

When you throw a ball straight up, does it spend more time going up, more time coming down, or the same time going up and down – taking into account both gravity and air resistance?

## Chance of Rain

You are driving to Seattle to meet some friends, and want to know whether you should bring an umbrella. You call up 3 of your friends who live there and independently ask them if it’s raining. Your friends like to…

## Seven Times the Sum of Its Digits

Which two-digit numbers are exactly equal to seven times the sum of its digits?

## Pigeonhole Principle

The Pigeonhole Principle is a simple and elegant concept: If you place more than n pigeons into n pigeonholes, at least one of the pigeonholes must contain more than one pigeon. More generally, if you need to make more than…

## Slowing and Shrinking

Remove one letter from the word “SLOWING” to make another valid English word. Repeat this step until you are left with just one letter, ensuring every step results in an English word. What words did you make in the process?

## Game the Coin Flip Game

A small company is losing money and the boss is looking for ways to cut costs. The boss is a foolish gambler, so he offers two employees the choice of either taking flat 10% pay cut, or playing the following…

## Secret Translation

The CIA intercepted some messages from a criminal organization, some in English and some in an unknown foreign language or code. As a CIA analyst and translator, you have figured out the following sentences and their English translations, but you…

## Queen’s Mini Tour

Starting from this position, can the queen touch or pass through all nine highlighted squares in just four standard chess moves?

## Bribing a Series of Guards

A criminal is planning an escape across a well-guarded bridge, which has a series of 9 guards, who each require a bribe of one coin in order to pass by them in either direction. The criminal can keep a stash…

## Complete the Words

P _ _ _ N TD E _ _ _ STS T _ _ _C _ _ _ E R Which 3-letter word can be inserted into all four lines above to form complete words?

## Take Back a Move Chess Puzzle

This creative Leonid Kubbel chess puzzle has white take back a move and then checkmate! White just made a move, but then realized there was a mate in 1 on the last move and missed it. What was white’s last…

## Flipping Every N-th

There are 100 face-down cards. The first person that passes by flips over every card, the 2nd person that passes by flips over every 2nd card, and so forth – the n-th person that passes by flips over every n-th…

## Street Number Puzzle

You were walking around on a major street with 5-digit street numbers (for example, 11213) and noticed one of the street numbers was special – any two consecutive digits formed a 2-digit perfect square (in the order the digits appeared…

## Cryptic Pattern Puzzle

Replace the ?’s in each of these to complete the puzzle: Part 1 “Asia” is H“Cuffs” is S“Ender” is I“Redness” is F“Fuchsia” is ? Part 2 “Using” is E“Desist” is I“Visits” is E“Design” is ? Part 3 “Gross” is W…

## Rigging a Vote

There are five candidates participating in an unusual election. There are four rounds of voting, and only two candidates participate in each round, with the winner moving on and the loser dropping out. This means first candidate 1 will run…

## Island of Blue Eyes

There is an island known for its people with blue eyes, yet there is at least one green-eyed person on the island. No one knows the color of their own eyes, as there are no reflective surfaces on the island…

## Five’s a Crowd

Try to place five points in (or on the perimeter of) an equilateral triangle with side length 10, as to maximize the distance between the points. What is the greatest possible distance between the two closest points?

## Burning Ropes

You have two lengths of rope that take exactly 60 minutes to burn. The ropes burn unevenly so if you cut the rope in half, burning a half will not necessarily take 30 minutes. How do you precisely measure 45…

## Boxes of Apples and Oranges

There are three identical boxes of apples and oranges, except one contains all apples, one contains all oranges, and one contains a mix. The boxes are labeled “apples”, “oranges”, and “apples and oranges” but all 3 boxes were labeled incorrectly!…