Mental Exercise

1. Mystery Letters. What property do the letters
c o s u v w x z
have that
a b d e f g h i j k l m n p q r t y
do not have?

2. Boring Metal. A metal cylinder has a circular hole drilled straight through it from the flat top to the flat bottom. The diameter of the hole is one half the overall diameter of the cylinder. All the shavings from the drilling of the hole are saved and weighed and found to be 4 ounces. Assuming the density of the metal was consistent throughout the cylinder, what is the weight of the cylinder after drilling?

3. Cherrie Pie. Grandma pulls down her three well worn mixing bowls from the cupboard the bowls being nestled one inside the other. As she separated them out on the counter she says, "I will make a cherry pie if you can place these twelve cherries into the three bowls such that there is an odd number of cherries in each bowl." Can you solve Grandma's puzzle?

4. Ten Logic. See if you can figure out which of the following ten statements is true and which are false.

1. Exactly one statement in this list is false.
2. Exactly two statements in this list are false.
3. Exactly three statements in this list are false.
4. Exactly four statements in this list are false.
5. Exactly five statements in this list are false.
6. Exactly six statements in this list are false.
7. Exactly seven statements in this list are false.
8. Exactly eight statements in this list are false.
9. Exactly nine statements in this list are false.
10. Exactly ten statements in this list are false.

5. Pig Pen. A farmer has a pig pen which can be represented by twelve equal line segments:

The farmer needs to divide the pen into two equal areas. He can only move two of the fences (line segments) and can add exactly two fences. What should the farmer do?

6. Loser Wins. There is a tale of a sheik who tells his sons to race each of their best camels to a distant city to determine who will inherit his fortune. He stipulates that the one who has the slower camel will win the inheritance. After wandering for aimlessly for days, they seek the advice of a wise man. They immediately rush to and mount the camels and take off at top speed to the city. What did the wise man tell them?

7. Language Equations. For example, 2 = H. of C. translates to: 2 = Houses of Congress. So now consider, 2 = H. in a W. And consider, 4 = W. on a C. Can you solve these?

Answers

1. Mystery Letters. The letters in the first group look virtually unchanged (except for size) when shown as uppercase letters.

2. Boring Metal. A circle half the diameter of the original circle has just one quarter of the area of the original circle. A cylinder can be thought of as a circle with thickness. So the drilled hole represents one quarter of the whole. The weight of the cylinder after drilling is 12 ounces.

3. Cherry Pie. Place one of the bowls so that it is nested inside the other. Place seven cherries in the nested bowls, and five cherries in the other bowl. The two nested bowls now contain an odd number of cherries (seven) as does the lone bowl with five.

4. Ten Logic. All of the statements are false except for the ninth one.

5. Pig Pen. Two line segments are moved to the upper left. The two lines are the added to separate the pen in two.

6. Loser Wins. The wise man told them to each mount the other brother's camel.

7. Language Equations. 
2 = Halves in a Whole.
4 = Wheels on a Car.