Varsity Math, Week 147

Varsity Math 147

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Welcome to Varsity Math, the weekly math puzzle column by the National Museum of Mathematics and featured each weekend in the Wall Street Journal.

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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.Quiz

Math Quiz

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.
Pool Party

Recent Weeks

Week 146: Mailing Problem & Pool Party, solutions to Find m and n & Escape Room

Week 145: Find m and n & Escape Room, solutions to Liar’s Club & Palindrome Times

Week 144: Liar’s Club & Palindrome Times, solutions to Staircase Numbers & Arithmetical Question

Week 143: Staircase Numbers & Arithmetical Question, solutions to A Golden Set & Combining Rule

Week 142: A Golden Set & Combining Rule, solutions to Sudoku Variant & Making 8 and 16

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.