## ________________

Another workout in logic is in store for the math team.

## ________________

### Knight Trap

A knight is placed on an infinite chessboard.

If it cannot move to a square previously visited, how can it be moved in as few moves as possible so that it has no more moves available?

### My Number is 136

Ana and Boris play a logic game. They both know that possibly identical positive integers, a and b, are chosen by a third party. Their product is written on Ana’s forehead and their sum is written on Boris’s forehead. Each can see the other’s number but not his or her own. After each sees the number on the other’s forehead, one says to the other, “There is no way you can know your number.” The other responds, “I now know my number is 136.”

What number is on Ana and what number is on Boris?

## Solutions to week 130

The thickness of the shell in The Size of Humanity would be about 9.14002103 ten-thousandths of a millimeter. This is less than a micron (= one millionth of a meter). In Fish Pond, the water level is 8 inches above the platform.

The Size of Humanity answer explained:
The surface area of the earth is A = 4πR2, where R = 6371 km. The volume of a shell of small thickness, t, is approximately V = At. In our case V = 7.4 × 109 × 63000 × 10-15 km3 = .4662 km3 so t = .4662/(4πR2) = 9.14002103 x 10-4 mm or 9.14002103 ten-thousandths of a millimeter.