Mind Game (2)

Stella Tse & Others

9 July 2013

Peter Wu: I would put 25 coins on each side. Assume the lighter coin is not in these 2 piles---perfect balance. The lighter coin is in the 30 coin pile. Place 10 of this pile onto each side---perfect balance or not. You will identify the 10 with the lighter coin. Now put 5 onto each side. You will identify pile of coins with the fake one. But which one is it?

Remove 1 coin from each side simultaneously. The shift direction of the balance arms will tell you which coin is the lighter one. Good enough for dinner for 20? It is a team work of 20!!!

Stella Tse: I like your answer Peter, and the dinner too.

Pony Ma: But that is more than 3 tries...

Peter

Cheung: Yeh! But my definiton of trials is different!

Stella Tse: Rod, here is a suggested solution from my son Eric ... it makes some sense.

He said that" my only thought was this: Round 1) split up the coins in half and place one half on one side in the middle of one arm of the balance and the other half on the other side, then measure how fast the balance accelerates somehow.Round 2) place all coins in individual piles all along the beam, then measure the rate of acceleration and use proportion to pinpoint the coin's location, though I'm not really sure the physics equations governing this type of motion operate in straight proportions since I forget the equations.... something to do with force, mass, time, acceleration, maybe centrifugal motion since the balance moves around a pivot. 

Round 3) same as 2 .

The end