A Multiplication Based Logic Puzzle

922 Boo!

Have you ever cut holes in a sheet, put it over your head, and jumped out in front of people as you hollered, “Boo!”? Today’s puzzle is made to look like a ghost. It’s a level 6, but don’t let that spook you! Attack the puzzle using logic, and after you solve it, you can claim to be a ghost-buster!

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

I think my ghost is cute. Maybe not as cute as …

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When 922 floats around in a different base, you may think you’re seeing an apparition:

922 becomes 1234 in BASE 9 because 1(9³) + 2(9²) + 3(9¹) + 4(9º) = 922.
922 becomes palindrome 262 in BASE 20

922 is also the sum of the 18 prime numbers from 17 to 89.

922 = 29² + 9², so 922 is the hypotenuse of a Pythagorean triple:
522-760-922, which is the same as 2(29)(9), 29² – 9², 29² + 9².
That Pythagorean triple is also 2 times (261-380-461).

  • 922 is a composite number.
  • Prime factorization: 922 = 2 × 461
  • 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 922 has exactly 4 factors.
  • Factors of 922: 1, 2, 461, 922
  • Factor pairs: 922 = 1 × 922 or 2 × 461
  • 922 has no square factors that allow its square root to be simplified. √922 ≈ 30.3644529

 

 

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