# Miscellaneous puzzles

A puzzle is a game, problem, or toy that tests a person's ingenuity. In a puzzle, one is required to put pieces together, in a logical way, in order to arrive at the correct solution of the puzzle. There are different types of puzzles for different ages.
Puzzles are often devised as a form of entertainment but they can also arise from serious mathematical or logistical problems. In such cases, their solution may be a significant contribution to mathematical research.
Solutions of puzzles often require the recognition of patterns and the creation of a particular kind of order. People with a high level of inductive reasoning aptitude may be better at solving such puzzles than others. But puzzles based upon inquiry and discovery may be solved more easily by those with good deduction skills. Deductive reasoning improves with practice.
Some notable creators of puzzles are Sam Loyd, Henry Dudeney, Boris Kordemsky and, more recently, David J. Bodycombe, Will Shortz, Lloyd King, and Martin Gardner. (Wikipedia)

Easier puzzle

## Is the bottle half full?

I have a bottle partly filled with water,
and I want to know if it's half full.

What is the simplest way to find out?

Answer: Just mark the level of the water, cap the bottle with your thumb and turn over the bottle.
If it's half full, the water will come up to the same level from the other end.

Average

## The Three Switches

There are three light switches downstairs, all of them currently in the OFF position. Each switch is connected to a different light bulb upstairs.

You would like to find out which light switch corresponds to which bulb. You may turn on any of the switches any number of times, but you may only go upstairs to inspect the bulbs only once.

How can you determine which light switch goes with which light bulb?.

Answer: Turn on switch 1 for a few minutes. then turn it off and turn on switch 2. Go immediately upstairs and inspect the lightbulbs.
If the light is on, it is connected to switch 2.
If the light is off but the bulb is warm, it is connected to switch 1.
If the light is off and the bulb is cold, it is connected to switch 3.

Very difficult puzzle

Easier puzzle

## Pie with 3 cuts

How do you cut a pizza pie into 8 equal slices with three straight cuts?

Step 1. cut the pizza in half.
Step 2. place one half on top of the other half.
Step 3. make a second cut to both halves at the same time leghtwise.
Step 4. make a third cut perpendicular to the last cut.
You end up with 8 pieces and you only made 3 cuts.

Average

## Pie with 4 cuts

What is the maximum number of pieces a pizza can have with four cuts?

(You are NOT allowed to put the cut piece(s) on top of the other.)

Difficult puzzle

## Pie with 6 cuts

The boarding house pie

Question:

Very difficult puzzle

## Pie with n cuts

What is the maximum number of pieces of pizza you can cut with n cuts?

(You are NOT allowed to put the cut piece(s) on top of the other.)

## Brain teaser challenges puzzle

There Is Something Wrong In This Image.
See If You Can Find It In Less Than 5 Secondsâ€¦

In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Explanation: With all the talk of doubling and halves, your brain jumps to the conclusion that to solve the problem of when the lily patch covers half the lake, all you have to do is divide the number of days it took to fill the lake (48) in half. It's understandable but wrong.
The right answer is that the patch would reach half the size of the lake on day 47.
The problem says that the patch DOUBLES in size every day, which means that on any day, the lily patch was half the size the day before. So if the patch reaches the entire size of the lake on the 48th day, it means the lily pad was half the size of the lake on day 47.