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Magic 45 - Puzzle of the week

2022-10-02T04:48:56.391Z

A number is to be broken down into four summands that have amazing properties. Is that possible?



Photo:

THE MIRROR

This week there is a problem that is hopefully only confusing at first glance.

It's about the number 45. It should be divided into four summands that have special properties.

You always get the same number if you:

  • 2 is added to the first summand

  • subtracts 2 from the second summand

  • divides the third summand by 2

  • multiplies the fourth summand by 2.

Is such a division of the number 45 possible?

What are the four summands?

Yes, there is a solution:

8, 12, 5, 20

.

The task with four unknowns seems unwieldy.

But with a simple trick, four unknowns become one.

With a we denote the number that is the result of the operations described above for the four summands.

Then we can express the summands themselves in terms of a: a-2, a+2, a/2, a*2.

The sum of these four summands must be 45.

So we write:

45 = a-2 + a+2 + a/2 + a*2


45 = 4*a + a/2


90 = 9*a


a = 10

Now we can easily calculate the four summands with a-2, a+2, a/2, a*2 - they are

8, 12, 5, 20

.

I discovered this easy number puzzle on the website denksport.de.

In case you missed a mystery from the past few weeks, here are the most recent episodes:

  • Perfectly arranged

  • Can these calculations add up?

  • Five points, three angles

  • Amazing exchange of digits

  • water march!

  • The jaunt

  • The card trick

  • How many elevators are needed?

  • Rook versus bishop

  • Beetles in love

Source: spiegel

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