# Age of Samantha and her grandchildren

Samantha is suffering from Alzheimer's and uses math to help remember things.

Samantha has two grandchildren.

Samantha youngest grandchild's age when raised to the power of the square root of her oldest grandchild's age is the age when Samantha was diagnosed with Alzheimer's.

Samantha knows her oldest grandchild was 2 years old when she was diagnosed with Alzheimer's.

If Samantha lives another 10 years the square root of her age then will be the same as the age of her oldest grandchild now.

Samantha's oldest grandchild is 5 years older than her youngest.

How old is Samantha and each or her grandchildren today? How old was Samantha when she was diagnosed with Alzheimer's?

• Probably should change the logic-puzzle tag to age-puzzle (the kind of logic used here is so general that it applies to most puzzles of all kinds)
– humn
Jun 9, 2016 at 5:53

$71, 9, 4$
The oldest grandchild's age is (presumably) a perfect square, and the square of her age is $10$ years older than a reasonable grandma age, so we can guess that she is now $9$. That makes the grandma $71$, and the younger child is $4$. So thus the grandma was $64$ when she was diagnosed.