Ken's POTW

Check(er)s and Balances
A small selection of quick problems this week:
1. 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.
2. 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?
3. 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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