## Ken's POTW

Check(er)s and Balances
A small selection of quick problems this week:
- Consider a small game of checkers, played on a 4x4 board.
Black starts with two pieces on A1 and A3. Red starts with
two pieces on D2 and D4. As in regular checkers, if a jump
is possible it must be taken. Red moves first. Does either
player have an advantage to win, or to at least not lose (stalemate)?
What if a restriction is added: For one player, if the previous two
moves have been to move one checker (a "king" or "crown")
from A to B, then from B to A, the
next move cannot be from A to B unless that is the only legal move.
- You have 4 weights weighing 2,3,5 and 7 pounds. The
problem is none of them are marked.
What is the least number of weighings you need using a
balance scale figure out which weights are which?
- What are the fewest number of weights you need to weigh any integral
number of pounds (from 1 to 40) on a balance scale?

Source:
1. Original. 2. Jason Telgren, who says it's public domain.
3. Sam Loyd.

Solution

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