#2             69. COINS AND GLASSES               

After buying his glass of beer, George arranged the six coins he received as change.

“Look at this!” he said to Bertie the barman. “A row of four, and a row of three. But I bet you can’t rearrange them to make two rows of four!”

Bertie gave up after a few minutes. Did you?

“Actually,” said Bertie, “I’m better with drinks. Look, here are five glasses, The problem is to rearrange them so that they are alternately one filled, one empty, one filled, one empty, one filled.”

“That’s no problem at all,” said George. “No problem to make them all empty either!”

“Ah,” said Bertie. “I haven’t finished. You are only allowed to touch or move one of the glasses!”
HINT 1

Think about what is not possible. What would two straight rows of coins in the plane require?
HINT 2

Think about the first problem. It was solved by ‘thinking outside the square’. Try to think craeatively about this problem too.
SOLUTION

Problem 1. Take the coin at the foot of the column, and place it on top of the coin at the intersection.

Problem 2. Take the second glass and pour its contents into the fifth glass.

Now, to celebrate the solution of both of these problems, ... !
EXTENSIONS

1. Problem solving often demands going beyond the expected. The first problem here presents as a problem in the plane. A solution involving the third dimension is therefore unexpected. In the second problem, the idea of pouring one glass into another is unexpected.

2. A problem of this sort which comes to mind is the following. You are given a 3 x 3 array of dots. Draw four lines in a continuous path to pass through all the dots. What is unexpected about this solution?