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.
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