Mathematical Curiosities: A Treasure Trove of Unexpected Entertainments by Posamentier Alfred S. & Lehmann Ingmar

Author:Posamentier, Alfred S. & Lehmann, Ingmar [Posamentier, Alfred S.]
Language: eng
Format: azw3
Publisher: Prometheus Books
Published: 2014-08-11T16:00:00+00:00

Hint: Mathematicians have been frustrated by this question, as they believe it requires thirteen hours, which would make it impossible for them to leave the cave with a flashlight having a battery life of only twelve hours. There is a solution with twelve hours!

PROBLEM 89

There are at least two ways of doing this problem: The poet's way or the peasant's way. Which will you select?

What is the sum of all the numbers formed by rearranging the digits of the number 975?

PROBLEM 90

A simple algorithm—but well camouflaged!

You can present this problem to friends, but you stand a possibility of losing the friendships because of the frustration that could develop in seeking a solution. Through hints along the way, you could even drive them mad.

The algorithm we seek assigns a natural number to any four-digit number as shown by the examples below. Your friends can select a four-digit number, and you (as the expert) can apply the algorithm to assign the appropriate natural number to this given four-digit number. By doing this so rapidly, it will clearly impress your friends but will also, while they seek a solution, add to their frustration.

The chart below is an example of the algorithm in action, assigning to each of the four-digit numbers a simple natural number from 0 to 9.

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