Difficulty – Hard

Hard brain teasers and puzzles

Difficulty - Hard, Simple Math

Consecutive Numbers Grid Puzzle

13
		10
	4	16
	7

The cells in this 4×4 grid puzzle contain the numbers 1-16 each once. There are two rules to the arrangement of the numbers:

Any two consecutive numbers must share a row/column (1 and 16 should be considered consecutive).
No row/column can contain three consecutive numbers.

Fill in the remaining numbers.

Difficulty - Hard, Interview Brain Teasers, Logic Puzzles, Number Theory

The Impossible Puzzle

This puzzle was coined the “Impossible Puzzle” by Martin Gardner, a famous math and science writer that liked to create and write about math games and puzzles. The puzzle is named as such because it appears to provide insufficient information to solve, but it is in fact solvable! Read on for the puzzle and the (very difficult) solution.

There are two distinct whole numbers greater than 1, we can call them x and y (where y > x). We know the sum of x and y is no more than 100.

Sam and Prada are perfect logicians. Sam (“sum”) is told x + y and Prada (“product”) is told x * y, and both of them know all the information provided so far.

Sam and Prada have this conversation in which they truthfully deduce the numbers:

Sam: I know Prada does not know x and y.
Prada: Well now I know x and y.
Sam: Ah, now I also know x and y.

Can you figure out x and y using this information?

View Solution

Difficulty - Hard, Geometry

Four Lines of Four Coins

Form four lines of four coins by moving exactly 3 of the coins below:

Rules:

Coins cannot be stacked on top of one another.
A line of five or more coins is still only considered one line.
The centers of the coins must be precisely on the same straight line, but can be anywhere on the line.
Lines can be any length, and can be horizontal, vertical, or diagonal.

Difficulty - Hard, Game Theory and Game Strategies, Probability

Truel

A truel is a three-way duel. The three participants take turns firing one shot at whichever opponent they choose, until only one is remaining.

Allison, Ben, and Chase are in a truel, and have varying degrees of accuracy: Allison has a 50% chance of hitting her intended target, Ben has a 80% chance, and Chase has a 100% chance. Allison gets to shoot first, then Ben, then Chase, and repeating in that order until only one person is remaining.

Assume that the accuracy of all participants are publicly known, and everyone is trying to maximize their chances of winning. What is Allison’s optimal strategy, and what is her likelihood of winning under that strategy?

Chess, Difficulty - Hard

Mate in 2 Chess Puzzle 1

White to play and mate in 2.

Difficulty - Hard, Interview Brain Teasers

Battery Test Puzzle

You have four good/new batteries and four bad/used batteries but don’t know which are which. You have a flashlight that uses two batteries, which will only work if both batteries are good – if it doesn’t work, you won’t know if both batteries are bad or just one.

How many pairs of batteries do you need to test to guarantee you find a good pair?

Chess, Difficulty - Hard

Chess Tactic Puzzle

Black is down significant material, but has a strong series of moves to turn things around. Can you find it?

Difficulty - Hard, Riddles and Lateral Thinking

Food with 5 Letters

I am a food with 5 letters.

Take away my first letter, and I become a form of energy.

Take away my first two letters, and I become something you need to live.

Rearrange my last three letters, and I become something you drink.

Difficulty - Hard, Geometry, Matchstick Puzzles

Make Five into Four

Move exactly 3 matches to make these five squares into four squares of equal size, without any matches left over.

Difficulty - Hard, Interview Brain Teasers, Logic Puzzles

Fake Coins Proof

You are a rare coins expert and have determined there are 7 fake coins out of 14 gold coins. Now you need to prove to the judge which ones are fake.

It is known that that real coins all weigh the same, fake coins all weigh the same, and fake coins weigh less than real ones (but are otherwise identical).

Using a traditional double-pan balance scale just 3 times, can you prove exactly which of the 14 coins are fake?

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