On a hike, twelve high school basketball players carried ten loaves of bread. Each varsity player carried one loaf; each junior varsity player carried a half loaf; and each first-year player carried a quarter loaf. How many players from each team were there, assuming that there was at least one player from each team?
Pre-Algebra
Spare Tire, Alaska
Ed traveled 5000 miles round-trip between home and Fairbanks in a car with one spare tire. He rotated tires at intervals so that when the trip ended, each tire had been used for the same number of miles. For how many miles was each tire used?
Alex Watt’s Will (Scotland)
Alex Watt, piano maker and friend to man, died in Edinburgh, Scotland, in 1849. He left the contents of his vault as follows: half to his devoted wife Millie, one-tenth to his cousin Sam, one-fourth to Stella’s great-grandfather Angus, who moved to Amsterdam and married royalty, and the remaining 94 pounds to the Firth of Forth Bagpipe Band in Edinburgh, of which both he and Sam had been faithful members (Alex a piper, Sam on the bass drum). How much did Sam inherit?
Stella’s Bookshelves
As we all know, Stella studied piano with the renowned Nadia Boulanger in Paris after World War II. In Amsterdam, in her studio, she has three shelves with books of four-hand piano music that she often plays with her husband Graziano (who needs to practice more). The top shelf contains 1/6 of all the scores. The middle shelf contains more than 2/5 of the scores, and the bottom shelf contains only four scores (but they’re thick ones). What is the smallest total number of scores that she might have on all three shelves?
Large Multiples of 17
What is the largest multiple of 17 that can be diplayed on an 8-digit calculator?
Broken Radical Key
The √ key on your calculator is broken. (So is the y½ subroutine.) How can you find √173 to 3 decimal places using your calculator and nobody else’s?
Sand Buying
A large sack of sand is $3.25 for 50 pounds; a small sack is $2.29 for 30 pounds. You need 170 pounds of sand. What’s the cheapest way to buy it?
Heap, Egyptian Equation
What may be the earliest note of an equation is found in the ancient Egyptian records of Ahmes in the following form: “heap, its two-thirds, its half, its seventh, its whole gives 97.” If we interpret “its two-thirds” as “two thirds of the heap” and assume that we are adding all of these amounts, we can find out how big the heap is. Proceed.
Man’s Long Life
Pebble lived 1/12 of his life as a small child and 1/6 more as a “youth”. Then he married Bloomie and lived happily 1/7 of his life plus 5 more years. Then they had a son, Nelius, whom, sadly, Pebble outlived by four years. Nelius lived to be 1/2 of Pebble’s final age. How old was Pebble when he died?
Digits in Number in Exponential Form
How many digits are there in the number N if N = 213 · 59?