On a table, are 50 quarters. 40 of them are tails up and 10 are heads up.
You are blindfolded, so you cannot see the quarters. Also, you are wearing gloves, so you cannot distinguish between heads up and tails up quarters by touching them.
You have to divide the quarters into two groups such that the number of heads up quarters in both the groups is the same. There is no restriction on the total number of quarters in each group or on the number of heads up quarters in each group. You are allowed to flip the quarters.
How can you accomplish this?
Solution: Divide the quarters into two groups of 10 coins and 40 coins and flip all the 10 coins in the smaller group.
Suppose there are x heads in the 10-coin group. You have:
10-coin group -> x heads, 10-x tails
40-coin group -> 10-x heads(since total heads=10), 30+x tails
When you flip all the coins in the smaller group you have:
10-coin group -> 10-x heads, x tails
40-coin group -> 10-x heads, 30+x tails
The number of heads in the two groups is the same.
Winner: Subodh Singh
Take any 10 coins out of the lot and flip them.
ReplyDeleteMake the rest as another lot.
You would have the same heads in both lots.