Last Fortnight's Solution

Challenge question #56 (31/07/2017)

Junior Question

Albert and Bec play a game involving $15$ game pieces. The game has the following rules:

  • The players take turns picking up pieces from the table.
  • $1$, $2$, or $3$ pieces must be picked up each time.
  • The player who picks up the last piece on the table wins.

It is Albert's turn first. What strategy should Albert use to ensure that he wins the game?


Senior Question

Three men, Arthur, Brian, and Charles went with their wives to an auction market to buy some sheep. Their wives' names were Rachel, Stef, and Tracy, not necessarily in that order. The average price that each person paid for their sheep was the same as the actual number of sheep that they bought. For example, if Arthur bought $A$ sheep at $$A$ each, he spent $$A^{2}$ altogether.

Arthur bought $23$ more sheep than Stef, and Brian bought $11$ more sheep than Rachel, and each man spent $$63$ more than his wife.

Who is married to whom?