1295 Mystery Level

This pinwheel-shaped puzzle is no little kid’s toy. The logic needed to solve it might be a mystery to see, but it is still there!

Print the puzzles or type the solution in this excel file: 12 factors 1289-1299

Here are some facts about the number 1295:

  • 1295 is a composite number.
  • Prime factorization: 1295 = 5 × 7 × 37
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1295 has exactly 8 factors.
  • Factors of 1295: 1, 5, 7, 35, 37, 185, 259, 1295
  • Factor pairs: 1295 = 1 × 1295, 5 × 259, 7 × 185, or 35 × 37
  • 1295 has no square factors that allow its square root to be simplified. √1295 ≈ 35.98611

Since 35 × 37 = 1295, we know that 1295 is one number less than 36².

1295 is the hypotenuse of FOUR Pythagorean triples:
399-1232-1295 which is 7 times (57-176-185)
420-1225-1295 which is 35 times (12-35-37)
728-1071-1295 which is 7 times (104-153-185)
777-1036-1295 which is (3-4-5) times 259

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