A Multiplication Based Logic Puzzle

Some bugs make creepy Halloween decorations. Other bugs, like ladybugs, might make a very cute costume.

Today’s puzzle looks like a bug, but there is no reason to run and hide from this one. Yes, it’s a level 5, so some parts of it may be tricky.

This is what you need to do to solve it: stay calm; don’t guess and check. Figure out where to put each number from 1 to 10 in both the top row and the first column so that the clues make the puzzle work like a multiplication table. Don’t write a number down unless you are absolutely sure it belongs where you’re putting it. Use logic, step by step, and this puzzle will be a treat.

Print the puzzles or type the solution on this excel file: 10-factors-914-922

When you put on a Halloween costume, you may look completely different.

When a number is written in a different base, it may look completely different. For example,
921 looks like repdigit 333 in BASE 17 because 3(17²) + 3(17¹) + 3(17º) = 3(289 + 17 + 1) = 3(307) = 921
(307 is 111 in BASE 17)

921 looks like palindrome 1H1 in BASE 23 (H is 17 base 10). As you might suspect, 1(23²) + 17(23¹) + 1(23º) = 529 + 391 + 1 = 921

When it’s not written in a different base, 921 looks pretty familiar. You can tell quite quickly that it is divisible by 3:

  • 921 is a composite number.
  • Prime factorization: 921 = 3 × 307
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 921 has exactly 4 factors.
  • Factors of 921: 1, 3, 307, 921
  • Factor pairs: 921 = 1 × 921 or 3 × 307
  • 921 has no square factors that allow its square root to be simplified. √921 ≈ 30.34798181

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