Member Avatar for quintoncoert

How about a game of math and logic puzzles. Ask a logical or mathematical question and if no one can answer within a certain amount of time the asker gives and explain the answer.

I shal go first. This is an older puzzle so some might have heard it before.

A scout infiltrate an enemy camp in order to count the number of cannon balls the enemy has. The enemy has been very helpful and has stacked the balls in a piramid with a square base. each layer of the piramid is of course smaller in square surface as the piramid gets higher until the last layer is only one ball big.

As he watch an enemy soldier aproaches and bring one more ball. Since there is no space for the last ball in this piramid the enemy troops break down the old piramid and build a new one which has a triangular base. In this new piramid the is one spot left on top of the piramid so that the last ball fits exactly.

Before the scout can count however they cover the piramid with a sail and post gaurds. How did the scout compute the number of balls without going near the gaurds.

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Member Avatar for joshSCH

He used an invisibility cloak?

Member Avatar for quintoncoert

>He used an invisibility cloak?

Ha! funny. seriously though. they were not invented yet during the time of canon balls! He used math.

visualize a three dimensional piramid.

squared base.
the top layer is one ball. the second layer is four balls since this the only way that the top ball can fit on top of the second layer. third layer is nine balls and so on and so on. try it with marbles. do the same for a piramid with a triangular base. if you add the balls together for both piramids( i.e. 1 + 4 + 9 etc ) for every layer your get a series for both piramids.
square based ( 1, 5, 14, etc)
triangular based ( 1, 4, 10 etc ).

eventually you reachd the point where the triangular based piramid has one ball more. that number is 56. that one more is the extra ball the soldier carried.

actually propper math creates two quadratic equations which cuts each other at two places and the number of balls could have been either of these two numbers. 56 is the lower of the two numbers.

i hope the math was not too irritating but this is geek's lounge yes?

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