NPR Sunday Puzzle (Jan 5, 2025): Math Fun in 2025Q: This week's challenge is s a numerical challenge for a change. Take the digits 2, 3, 4, and 5. Arrange them in some way using standard arithmetic operations to make 2,025. Can you do it?
I'm not sure how to clue this... but I'm going to say 865 or 2619.
Edit: One possible order to the digits is 3452. The prime factorization of 3452 is 2² x 863. Adding the unique prime factors gives 865.
Another possible order is 5234. Its prime factorization is 2 x 2617. Adding the prime factors gives 2619.
A: If you just take the prime factorization of 2025, you have the answer.
3⁴ x 5² = 2025, or 5² x 3⁴ = 2025.
Note: You could also just use 25 in place of 5²
(3⁴ x 25 or 25 x 3⁴).
I'm sorry to everyone for the
times I had to use my moderator
powers.
One comment I hated to delete was the one about the sum of the cubes of the first 9 integers. (1³ + 2³ + 3³ + ... + 8³ + 9³ = 2025). It also included the related fact that the sum of the first 9 integers squared gets the same result (1 + 2 + 3 + ... + 8 + 9)² = 2025.
This is actually true for the first 'n' integers that the sum of the cubes is the square of the sum. (1³ + 2³ + 3³ + ... + n³) = (1 + 2 + 3 + ... + n)².
Here's a
visual proof for the first 5 integers.