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### Mathematical Reasoning Puzzles

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

## #21

A toy store ordered 7 small bags and 18 large bags of identical marbles. When the marbles arrived, it was discovered that the bags had broken during shipping, and all 233 of the marbles were rolling around loose in the box. How was the store's manager was able to determine how many marbles were supposed to go in each of the small bags and how many were supposed to go in each of the large bags?

Solution

## #22

A box contains two quarters. One is a double-headed coin, and the other is an ordinary coin, heads on one side, and tails on the other. You draw one of the coins from a box and look at one of the sides. Assuming it is heads, what is the probability that the other side shows heads also?

Solution

## #23

You're a cook in a restaurant in a quaint country where clocks are outlawed. You have a four minute hourglass, a seven minute hourglass, and a pot of boiling water. A regular customer orders a nine-minute egg, and you know this person to be extremely picky and will not like it if you overcook or undercook the egg, even by a few seconds. What is the least amount of time it will take to prepare the egg, and how will you do it?

Solution

## #24

I'm going to buy one-cent, two-cent, three-cent, five-cent, and ten-cent stamps. I'm going to buy four of each of two sorts, and three of each of the rest, and I have exactly enough to buy them -- just this handful of dimes. How many of each type am I going to buy?

Solution

## #25

If a boy and a half can eat a hot dog and a half in a minute and a half, how many hot dogs can six boys eat in six minutes?

Solution

## #26

Five pirates raid the ship of a wealthy bureaucrat and steal his trunk of gold pieces. By the time they get the trunk aboard, dusk has fallen, so they agree to split the gold the next morning.

But the pirates are all very greedy. During the night one of the pirates decides to take some of the gold pieces for himself. He sneaks to the trunk and divides the gold pieces into five equal piles, with one gold piece left over. He puts the gold piece in his pile, hides it, puts the other four piles back in the trunk, and sneaks back to bed.

One by one, the remaining pirates do the same. They sneak to the trunk, divide the coins into five piles, with always one coin left over. Each pirate puts the gold coin in his own pile, hides it, and puts the remaining four piles back in the trunk.

What is the smallest number of coins there could have been in the trunk originally?

Solution

## #27

Reason why 30414093201713378043612608166064768844377641568960512078291027000 cannot possibly be the value of 50 factorial, without actually performing the calculation.

Solution

## #28

What two numbers have a product of 48 and, when the larger number is divided by the smaller, a quotient of 3?

Solution

## #29

A man has \$1.15 in six coins. He can't make change for a dollar, a half dollar, a quarter, a dime, or a nickel. What coins did he have?

Solution

## #30

Two boys sell apples. Each sells thirty apples a day. The first boy sells his apples at two for fifty cents (and therefore earns \$7.50 per day). The second boy sells his apples at three for fifty cents (and therefore earns \$5.00 per day). The total received by both boys each day is therefore \$12.50.

One day, the first boy is sick, and the second boy takes over his apple selling duties. To accommodate the differing rates, the boy sells the sixty apples at five for a dollar. But selling sixty apples at five for a dollar yields only \$12.00 earnings at the end of the day. What happened to the other fifty cents?

Solution