Spermatikos Logos #3

Hey everyone, I'm back again. Hope you've all survived as well. I only received two submissions this week, so I guess I'm not the only one who's been attacked by midterm stress. Thanks to both Lisa Harpur and Greg "Hologrami" Taylor for submitting solutions to Logos #2. Greg got the correct solution the way I figured it. Lisa actually found a solution that was different from mine, but still correct (forgive me, I was tired and didn't check it properly when I made it). By random draw, Greg gets the prize. Go pick it up in the MathSoc office. Submissions for Logos #3 are due November 16^th, at 6:30pm in the BLACK BOX... Where's the BLACK BOX? Good question. It's hiding in the depths of the mathNEWS office. So, you can either e-mail your submissions to me at gngarbet@uwaterloo, you can slip them under the door of the office (although if you do this it may not get found anyway — ask Greg), or you can drop it off at the MathSoc office.

Solution A to Logos #2

Solution B to Logos #2

This Week's Puzzle

As part of this exciting feature issue, I've decided to make a logic problem that fits the theme. It's loosely based on a game show from Square One, called But Who's Multiplying! (No comments from Snuggles, please.) The way it works is as follows: the contestants get two numbers at a time, and they have to multiply them together to get a number on the board, and that square is highlighted with their team's colour. The rest of it is reminiscent of Bingo. Anyway, in my world the squares are all mixed up. Yes, I know some of them are prime, but it's like that on the show too. (mutter, mutter) What you have to do is figure out where on the board all the numbers are. It's not too hard, there are only 25 squares to work with... The columns are labelled (left to right) A, B, C, D, and E, and the rows are labelled (top to bottom) V, W, X, Y, and Z. Um... yeah, that should be it. Contestants, are you ready? Go!!

1. The numbers on the board are from 2 to 26, in scrambled order.
2. The four corners of the board are (in no particular order): a prime number, a perfect number, a perfect square, and one of the numbers mentioned in clue #1.
3. Every column with a "6" also has a "9", and does not have a "7".
4. The number 17 has odd numbers on all three sides.
5. The sum of one of the diagonals is 44.
6. The number 3 is directly above a prime number, directly below a multiple of 7, and between two consecutive numbers (in some order), neither of which are prime.
7. The 10 is higher on the board than the 13, which is higher than the 20.
8. The number 23 is directly below and between three consecutive numbers (in some order).
9. The number 7 is between two numbers which are reflections of each other (like 68 and 86).
10. The number 2 is directly above the 26.
11. The 22 is somewhere left of the 5, which is somewhere left of the 11.
12. The number 6 is somewhere above and to the left of the 12, which is somewhere above the 18.
13. Any prime number ending in 3 or 1 is not in a corner.
14. Three of the perfect squares are in the same row. The fourth shares a column with one of the other three. None of them are adjacent.
15. The number 19 is diagonally next to (and to the right of) the 7.
16. Three of the four corners of the board end in the same number.
17. The number 21 is directly between both of its divisors.
18. The number 4 is somewhere left of the 8, which is directly above the 16.
19. Every row with a "9" also has a "4". There is no "4" in columns A or E.
20. The number 4 is directly to the right of a prime number, and directly to the left of a multiple of six.
21. There are three prime numbers on the bottom row.

Gigi Garbett
gngarbet@uwaterloo.ca