I keep feeling like there's more to this.Q: Think of a familiar two-word phrase that means "a secret mission". Move the last letter of the first word to the start of the second word. The result will be two words that are synonyms. What are they?
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On my map, the WATER is BLUE and the LAND is GREEN. Also, AGUA is a Spanish word we know to be WATER, while TERRA is a Latin word we know to be EARTH or LAND
I was sure the answer was going to be NICAR/AGUA, but sadly NICAR didn't become WATER.Q: Think of a well-known international location in nine letters. Take the first five letters and shift each of them 13 places later in the alphabet. The result will be a synonym for the remaining four letters in the place's name. What place is it?
On my map, the WATER is BLUE and the LAND is GREEN. Also, AGUA is a Spanish word we know to be WATER, while TERRA is a Latin word we know to be EARTH or LAND
A: GREENLAND --> TERRA, LAND
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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.
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.
I'm not sure how to clue this... but I'm going to say 865 or 2619.Q: 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?
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.I'm sorry to everyone for the times I had to use my moderator powers.
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).
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.
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