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# Grandfather's grandchildren

When I turned fifty my first grandson was born. Now that I am on my way to seventy, I have many more: "Each of my children has as many children as brothers and the combined number of my children and grandchildren is exactly my age."

How old am I?

#### Solution

There are several ways to solve this problem. We will test by scoring. Suppose you have 5 children. If each one has as many children as brothers, he has 4 children, so that in total he will have 5 * 4 = 20 grandchildren. The sum of grandchildren and children is 20 + 5 = 25, which is far from the age they should be that will be greater than 50 and less than 70.

If we continue to test, we get that in the case of 7 children, we get 7 * 6 = 42 grandchildren and 49 as a combined sum. If we test with 8 children we find the valid answer, which is 56 grandchildren and 64 years of age since if we continue to increase the number of children the number of grandchildren increases and therefore the total sum since with 9 children the age of Grandfather would be 81 years old and left out of the possible age range. Therefore 8 children is the only possible answer. Will be 64 years old, 8 children and 56 grandchildren. Each son has 7 brothers and 7 children.