Today’s Puzzle:

The celebrated author of Math Play, Libo Valencia, recently wrote a post on how he uses mathplay to help his nine-year-old daughter learn the multiplication table. One of the playful things they did together was find objects around the house to represent several perfect squares. For example, they happened to have some small bright yellow hexagons in their house and they used six of them to show that six times six is thirty-six. If you don’t have any bright yellow hexagons at your place, you probably have some hexagon-shaped nuts and/or bolts you could use to show 6 × 6 = 36.

All but two of the clues in today’s puzzle are perfect squares, so I’m dedicating this puzzle to Libo’s daughter. Square number thirty-six is a clue three times in the puzzle. The rules of the puzzle won’t allow 6 × 6 to be the factors for all three of them, however. I’m sure you can figure the puzzle out, anyway. Just make sure you’re having fun doing it. There is only one solution.

Factors of 1774:

• 1774 is a prime number.
• Prime factorization: 1774 is prime.
• 1774 has no exponents greater than 1 in its prime factorization, so √1774 cannot be simplified.
• The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1774 has exactly 2 factors.
• The factors of 1774 are outlined with their factor pair partners in the graphic below.

More About the Number 1774:

1774 is a palindrome in a couple of bases:
It’s 626 in base17 because 6(17²) + 2(17) + 6(1) = 1774, and
it’s 383 in base23 because 3(23²) + 8(23) + 3(1) =1774.