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?

## Puzzles, Riddles, and Systematic Thinking

## Muffins

Milly Miffin made one muffin more than Molly’s mother made, and Milly Miffin’s mother made one muffin more than Molly made; and Molly’s mother and Milly and Milly’s mother and Molly made 50 muffins (total), but Molly’s mother and Milly made 4 muffins more than Milly’s mother and Molly made. So murmur how many muffins Milly made.

## 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.

## Ship and Boiler Ages

The good ship Gemini is twice as old as its boiler was when the ship was as old as the boiler is now. If the sum of their ages is 49 years, how old is the ship? How old is the boiler?

## Complicated Ages (Andrea, Bonnie)

Andrea and Bonnie are comparing their ages; they find that Bonnie is as old as Andrea was when Bonnie was as old as Andrea had been when Bonnie had been half as old as Andrea is now. If the sum of their present ages is 44 years, then what is Andrea’s 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?

## Birthday Present (Dimes, Quarters)

Hartley and Bertha are pooling their money to buy their mother a birthday present. (Her birthday, by coincidence, turned out to be the day she was elected to the school board.) The two have $20.25 between them. Hartley has all of his money in dimes and Bertha’s is in quarters. Hartley has twice as many dimes as Bertha has quarters. How much money is Hartley contributing?

## Divide Dollar Among 12 Kids

A woman divided $1 among 12 children. Boys got 7 cents; girls got 9 cents. How many girls were there?

## Wealth Redistribution

The kingdom of Syldavia has five economic classes. Feeling one day that there is too great a disparity among the wealth of the classes, the King asks his Finance Minister to devise a plan to redistribute the wealth of the classes. The FM proposes that the wealth of the top two classes be averaged, then the wealth of classes 2 and 3 be averaged, then the wealth of classes 3 and 4 be averaged, and finally that the wealth of classes 4 and 5 be averaged—a four-step process. The King likes the sound of the plan, but suggests that the progression should be from the lowest classes upwards. (In either case, the result will be a four-class system.) Which of the two plans should the lowest class prefer? Why?

## Mike’s Age

Mike’s age right now is exactly 3 times his age 3 years hence minus 3 times his age 3 years ago. How old is Mike right now?