Welcome to Varsity Math, the weekly math puzzle column by the National Museum of Mathematics and featured each weekend in the Wall Street Journal.
Alternative Sum and Product
The sum of the digits from 1 to 9 is 45 and their product is 9 factorial = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 = 362,880.
Find another set of nine single-digit numbers with a sum of 45 and a product of 9 factorial. Digits may be repeated.
Aileen, Brian, Laurie and Sue have just received the results of a math quiz they took. Each problem correctly solved earns the same number of points.
Aileen: Our average was half a perfect score.
Brian: I got three wrong.
Laurie: I got nine correct.
Sue: I got eleven wrong.
How many problems did Aileen get correct?
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Solutions to week 146
In Mailing Problem, the coach’s package had a volume of 360 with dimensions (9, 8, 5). Prior to that, the coach had considered a box with dimensions of (10, 9, 4). In Pool Party, the coach’s yard is 34 feet by 34 feet.
Pool Party answer explained:
Let P = (9, 2) be the coordinates of the corner of the walkway that touches the pool and let C = (r, r) be the coordinates of the center of the pool. Then r2 = (r-9)2 + (r-2)2. This leads to r = 17 ft., so the yard is 34 ft. by 34 ft. The other root with r = 5 ft. would have the pool overlap the walkway.
Links to all of the puzzles and solutions are on the Complete Varsity Math page.
Come back next week for answers and more puzzles.