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### Mathematical Reasoning Puzzles

These puzzles require both logical and mathematical reasoning. Can you solve them?

## #31

The expression, "Six of one, half a dozen of another," is commonly used to indicate that two alternatives are essentially equivalent, because six and a half dozen are equal quantities. But are "six dozen dozen dozen" and "a half dozen dozen dozen" equal?

Solution

## #32

Two alligator breeders were talking one day, and in the course of their conversation they noticed a curious coincidence. If alligator breeder #1 were to sell alligator breeder #2 seven alligators, then breeder #1 would have exactly as many alligators as breeder #2. On the other hand, if alligator breeder #2 were to sell alligator breeder #1 seven alligators, then breeder #1 would have exactly twice as many alligators as breeder #2. How many alligators did each breeder have?

Solution

## #33

How can you express the number 100 using six nines and no other digits?

Solution

## #34

A drove of sheep and chickens have a total of 99 heads and feet. There are twice as many chickens as sheep. How many of each are there?

Solution

## #35

An eccentric individual makes it is life's work to tie a rope around the earth's equator. He buys a lot of rope and makes the attempt. A rival of his, not to be outdone, decides he wants to tie a rope around the earth's equator that is elevated from the ground by one yard at all points along the rope. How much more rope does he need? Assume the earth is perfectly spherical.

Solution

## #36

A fish is fifteen inches long. Its head is as long as its tail. If the head were twice as long as it really is, the head and tail would together be as long as what's in between. How long is each part of the fish?

Solution

## #37

A man has 100 coins (there are no quarters or nickels) that add up to \$5.00. How many coins did he have of each denomination?

Solution

## #38

One boy can eat 100 chocolates in half a minute, and another can eat half as many in twice the length of time. How many chocolates can both boys eat in 15 seconds?

Solution

## #39

Potatoes are made up of 99% water and 1% "potato matter." Jack bought 100 pounds of potatoes and left them outside in the sun for a while. When he returned, he discovered that the potatoes had dehydrated and were now only made up of 98% water. How much did the potatoes now weigh?

Solution

## #40

You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?

Solution