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January 1, 2015

Grandpa's Age Puzzle

Two boys don't know age of each other, one day they met grandpa and asked him about his age. Grandpa said:"The addtion of digit in tens place and the digit in ones place of my age is equal to the subtraction of digit in the tens place and the digit in ones place of age of one of you." The two guys thought hard, but didn't figure it out. The second day, they came to ask grandpa again, grandpa said:"My age is equal to the multiplication of the addition and subtraction of your ages." The two guys could not figure it out. The third day, they came to grandpa, grandpa said:"My age = (age of one of you)*7 - (age of the other)*4" The two poor boys still could not figure it out, the forth day, grandpa said:"One of you, whose age I didn't refer to in the first day, exchange his age's digit in tens place with digit in ones place, then minus the addition of the digit in tens place and the digit in ones place, the result is equal to my age." Can you figure out grandpa's age?


Paul P. Mealing said...

I admit this one has stumped me. One has to solve a quadratic equation with rather large numbers and there are a number of possibilities therefore a number of quadratic equations (at least 8, more like 16). I gave up after trying the 2 most obvious contenders.

Regards, Paul.

Paul P. Mealing said...

I've spent hours on this, an evening and the best part of a morning.

Actually, some of the possibilities eliminate themselves because they're negative or fractions. That left me with 4 quadratic equations but none of them gave rational solutions. Obviously, I've made a mistake but I wasn't able to find it.

Regards, Paul