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Math Puzzles
Math Puzzles

Here are some math puzzles that I believe help illustrate some thought processes similar to hacking a target system.  See if you can answer them.  None of them should require calculus or really any formal mathematics; a little logic should suffice!

 

Monkeys & Doors

There are 100 doors, all closed and numbered 1-100.

There are 100 monkeys.

The monkeys are sent one by one to change the state of a door (open to closed vs. closed to open).

Monkey 1 opens every door (1, 2, 3, 4...)

Monkey 2 changes the state of every other door (2, 4, 6, 8, 10...)

Monkey 3 changes the state of every third door (3, 6, 9, 12...)

And so on for monkeys 4-100...

After the monkeys make all their changes, what is the state of door N?  Give me a formula for N.

 

Children Ages

Two women are walking down the street.

The first woman says... "I forgot the ages of your three children."

The second woman says... "The product of their ages is 36."

The first woman says... "I still don't know their ages."

The second woman says... "The sum of their ages is your street address."

The first woman says... "I still don't know their ages."

The second woman says... "The oldest has red hair."

How old are the children?

 

Island of the Blue-Eyed People

There is an isolated island in the middle of the sea... On this island, people who have blue eyes kill themselves.

Because of this, no one talks about eye color, and there are no reflective surfaces on the island.

The island inhabitants are inherently logical geniuses and trust everything everyone says.

When someone decides to kill him/herself, he sleeps on it first, and then commits suicide the next morning.

The meet every morning after the death time and look at each other.

Suppose an evil demon arrives on the island and says, "At least one person on this island has blue eyes".

What happens if there are N blue-eyed people on the island?

 

Billiard Balls

You have 8 billiard balls.

Seven weigh exactly the same; one is heavier.

You also have a balancing scale.

How can you find the heavy ball in only 2 weighings?

 

Burning Joss Sticks

You have 4 joss sticks.

They burn unevenly. Non-linearly... all differently...

Each one burns for 1 hour.  All the sticks burn at different rates, but for a total of one hour each.

You need to measure precisely 1 hour 45 minutes using these sticks.

You have no watch, sundial, or any other timepiece.

You just have four sticks and matches.

No electrician or extension cord... or cell phone...

 

Lightbulb and Switches

There is one incandescent light bulb in an attic.

In the basement, there are three switches, each of which can be either on or off.  The switches are completely independent of one another.

One switch controls the light in the attic.

How can an electrician determine which switch controls the attic light bulb with only a single trip to the attic and no trip back down?

(You can't send another person or use any other equipment, like extension cords...)

 

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©Copyright 2004, Ed Skoudis