Chapter P.1, Problem LC

LINKING concepts... For Individual or Group Explorations

Number Puzzles

Puzzles concerning numbers are as old as numbers themselves. The best number puzzles can be solved without a lot of mathematics, but that does not necessarily make them easy.

a) Think of a number, and add $\langle \text{em}\rangle \frac{2}{3}\langle /\text{em}\rangle$ of this number to itself. From this sum, subtract $\langle \text{em}\rangle \frac{1}{3}\langle /\text{em}\rangle$ of its value and say what your answer is. From youranswer subtract $\langle \text{em}\rangle \frac{1}{10}\langle /\text{em}\rangle$ of your answer. You will now have your original number (Rhind papyrus. 1849 B.C.). Explain why this works.

b) Think of a number between 1 and 10. Think of the product of your number and 9. Think of the sum of the digits in your answer. Think of that number minus 5. Think of the letter in the alphabet that corresponds to the number you are thinking about. Think of a stale that begins with the letter. Think of the second letter in the state. Think of a big animal that begins with that letter. Think of the color of that animal. The color is gray. Explain.

c) Sandy has one quart of grass seed and one quart of sand, each stored in one- gallon containers. Sandy pours a little seed into the sand and shakes well. She then pours the same amount of the mix back into the container of seed so that both containers again contain exactly one quart. Is there more sand in Sandy’s seed or more seed in Sandy’s sand? Explain.

d) In each cell of the second row of the following table put one of the digits 0 through 9. You may use a digit more than once, but each digit in the second row must indicate the number of times that the digit above it appears in the second row.

0	1	2	3	4	5	6	7	8	9