For The Mathematically Inclined

For The Mathematically Inclined

anil saigal
10/08/2014

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?

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Solutions from 9/25/2014

Problem #1

The product of three consecutive odd numbers is 357,627. What is the smallest of the three?

Problem #2

A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they?

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

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