For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
10/22/2014

Problem #1

Can you find five consecutive whole number that are all positive and such that the sum of the squares of the two largest numbers is equal to the sum of the squares of the three smallest?

Problem #2

Use each digit 0 through 9 exactly once to form two five-digit numbers that when multiplied produce the largest quantity.

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Solutions from 10/09/2014

Problem #1

Find all sets of four positive consecutive integers such that the sum of the cubes of the first three is the cube of the fourth.

Problem #2

23 = 2³ + 2³ + 1³ + 1³ + 1³ + 1³ + 1³ + 1³ + 1³

Only one other integer requires nine cubes of positive integers to represent its value as a sum of cubes. This other integer is between 200 and 300. Can you find it?

Congratulations to Abhimanyu Bhargava and Saba Lateef, who were the winners of the last set of puzzles.

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