## Defined Operations 1; Do Composition

Suppose the operations “#” and “t” are defined so that:

6 # = 20; 2 # = 4; 10 # = 36; and 5 t = 4.5; 10 t = 7; 8 t = 6.

Then what is n if 3 # # t = n?

## Heads and Feet (Easy)

In the barnyard there are some cows and some chickens. When asked to count them, Marty came back and said that the number of legs, total, was 84 more than twice the number of heads. So how many of each kind of animal are there?

## Supermarket, Apples

The Superduper Supermarket has 128 crates of apples that have just arrived at the loading dock. Each crate contains at least 120 apples and at most 144 apples. What is the largest integer n you can find such that there must be at least n crates containing the same number of apples? (This means that, even if you make the number of apples in each crate as different as you can possibly make them, there are still going to be n crates with the same number of apples.)

1. 4
2. 5
3. 6
4. 24
5. 25

## Kite Strings

Buzz has three kite strings averaging 6600 feet in length. None is less than 6200 feet long. How long can the longest be?

## Garden Crops

A large organic nursery has somewhere between 3 and 6 (inclusive) garden plots of herbs when it closes for the season in the fall. In each plot there are between 20 and 30 (inclusive) rosemary plants. If, typically, 10% of those plants don’t winter over successfully until spring, what would be the largest number of plants that could be lost during the winter?

## Pet Rocks

The town of Ware has exactly 5000 families. Every family has 0, 1, or 2 pet rocks. Every pet rock belongs to a family. Most families have 1 pet rock. Exactly half of the remaining families have 2 pet rocks. How many pet rocks are there in Ware?

## Stationery

Shawn and Rhonda bought identical boxes of stationery. Shawn used hers to write 1-sheet letters and Rhonda used hers to write 3-sheet letters. Shawn used all of the envelopes and had 50 sheets of paper left, while Rhonda used all of the paper and had 50 envelopes left. The number of sheets of paper in each box was:

1. 150
2. 125
3. 120
4. 100
5. 80

## Ages as Perfect Square

Gil is 17 years older than Sheila. If his age is written after hers, the result is a 4-digit perfect square. The same statement will also be true 13 years from now. Find Sheila’s present age.

## Monkey and Rope

A piece of rope is hanging over a pulley. A weight is at one end of the rope and a monkey is hanging at the other end, scratching himself. The monkey and the weight are exactly level with each other. The monkey’s age and the age of his mother total seven years. The monkey weighs as many pounds as his mother is years old. Four feet of rope weighs one pound.

The monkey’s mother is one third again as old as the monkey would be if the monkey’s mother were half as old as the monkey will be when the monkey is three times as old as the monkey’s mother was when the monkey’s mother was three times as old as the monkey was then.

The weight of the weight and the rope together come to twice the difference between the sum of the weight of the weight plus the weight of the monkey and the weight of the weight.

How long is the rope?