Difficulty – Hard

Hard brain teasers and puzzles

Difficulty - Hard, Rebus

Got Hero Hero Puzzle

What common word or phrase is this rebus referring to?

GOT GOT GOT GOT HERO HERO HERO HERO HERO HERO HERO HERO HERO HERO

Click to show solution

Forgotten heroes (“four got ten heroes”)

Difficulty - Hard, Geometry, Matchstick Puzzles

Four Squares Match Puzzle

Move exactly 2 matches to make these five squares into four squares of equal size, without any matches left over.

Difficulty - Hard, Number Theory

Polydivisible Number

A polydivisible number is a number for which the first n digits form a number evenly divisible by n for all n between 1 and the number of digits of that number.

In other words, the first 2 digits form a number divisible by 2, first 3 digits form a number divisible by 3, first 4 digits form a number divisible by 4, etc. for all of the digits of the number.

Can you arrange the digits 1-9 to form a 9-digit polydivisible number? Each digit 1-9 must be used exactly once.

Difficulty - Hard, Game Theory and Game Strategies, Logic Puzzles

Two friends are playing a game with two boxes of chocolates. They take turns taking out some number of chocolates from the boxes, and whoever takes the last chocolate wins. Each turn they can take chocolates one of two ways:

Take any number of chocolates from a single box
Or take an equal number of chocolates from each box

If there are 25 chocolates in one box and 35 in the other, what is the winning strategy?

View Solution

Difficulty - Hard, Probability

Vacant Room Probability

Your workplace has a phone room for employees to quietly make personal calls. The room has no windows, just a sign that can be switched from “Vacant” to “Occupied”. However, employees differ in how consistently they use the sign:

1/2 of them always switch to “Occupied” when they enter and “Vacant” when they exit.
1/4 of them ignore the sign altogether – the sign will always read the same before, during, and after their visit.
1/4 of them always switching to “Occupied” when they enter, but always forget to switch back to “Vacant” when they exit.

If the room is actually occupied exactly 1/2 of the time, what is the probability the room is actually vacant when the sign reads “Vacant”?

Cryptography and Codes, Difficulty - Hard

Break the Cipher

The CIA is tracking a criminal organization and have reason to believe they are about to launch some sort of attack on New York City. One morning, they intercept this message, can you break the cipher and figure out what it means?

8 HIJP
11 IATC
2 BEIO
7 NTYH
4 AAWC
15 LLAT
12 NOML
6 TONF

Difficulty - Hard, Rebus

Rebus Puzzle 7

What common word or phrase is this rebus referring to?

FULL OF

Solution

Full of baloney (“below knee”)

Difficulty - Hard, Geometry, Matchstick Puzzles

Four Triangles with Matches

Move exactly 3 matches to make these three equilateral triangles into four equilateral triangles of any size, without any matches crossing or overlapping.

Difficulty - Hard, Interview Brain Teasers, Logic Puzzles

Pirate Survivor Puzzle

The democratic pirates are at it again! Since last time, they have become very successful and have now expanded to 100 pirates. They decide this is too large of a group for plundering, so true to their democratic roots, they want to settle it with a vote:

They vote on whether to kick out the newest (least senior) pirate.
If a majority votes “aye”, then the newest pirate is kicked out, and the process repeats with the remaining pirates.
If half or more of the remaining pirates vote “nay”, then the vote is over and everyone remaining is safe.

Each pirate wants to stay in the group, but if that is assured, they would prefer to kick out as many other pirates as possible (fewer ways to split the treasure).

How many pirates will remain at the end of this process?

Algebra, Difficulty - Hard, Number Theory

Sum of Squares

If x is an even integer that can be written as the sum of two perfect squares, prove that x / 2 can also be written as the sum of two perfect squares.