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.
Puzzles, Riddles, and Systematic Thinking
Cows, Horses, Sheep in Pasture
Kurt, Chris, and David paid a total of $100 to buy a pasture. They split up the cost according to the amount of grass their animals would eat. Kurt put in 9 horses; David put in 12 cows for twice the time; and Chris put in some sheep for 2.5 times as long as David’s cows. If Chris paid half the cost of the pasture, how many sheep did Chris have, and how much did Kurt and David each pay, if 6 cows eat as much as 4 horses and 10 sheep eat as much as 3 cows in a given amount of time?
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?
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?
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?
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?
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?
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.
Radical of Year of Birth
Stella’s grandfather was born during the 19th century. The square root of the year he was born, plus the square root of the year that Stella’s cousin Elspeth was born, equals the age of Stella’s grandfather when he died. So in what year did her gramps die, how old was he at his death, and how old is Elspeth now?
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?