Moneybags

While the snow was lightly falling on the ground outside Grandfather Pennywise's large mansion, he called to all his grandchildren to gather round the big easy chair in his den. Excitement was in the air, because they knew what was coming. The grand tradition was about to be enacted for another year. Dear old rich Grandfather "Moneybags" (as the children lovingly called him) always gave them money at Yuletide.

Grandfather always did so in an unusual, unique way, he gave to each of his grandsons as many dollars as there were grandsons, and to each of his granddaughters as many dollars as there were granddaughters.

After the envelopes containing each child's portion had been handed out, Linda exclaimed, "Grandad, you've given out $841 this year! Thank you!"

Of course, every grandchild (except the newborns) rushed to their grandfather to give him a hug and wish him a very Happy Holiday.


How many hugs did the kind old gentleman receive?


Good Luck Ms. L.

Here is the solution for this problem.


This problem was connected to our work with the Pythagorean theorem. The first solution was:



s^2 + d^2 = 841


where s = the number of grandsons (the dollars each boy would receive),
and d = the number of granddaughters (the dollars each girl would receive).


B² + G² = 29²

That is just a simple A² + B² = C².  20 and 21. Now, we know that there are more girls than boys, so G = 21 and B = 20.  Since there are 41 kids, the grandfather would receive 41 hugs if he got one from each grandchild, but the problem states that the newborn twins did not give him a hug, so he only received 39 hugs.