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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.*

### 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 r^{2} = (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.

## 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.