Outcomes and Nim

Questions 1 to 5 of 8

1. 1. Piles 1, 2 and 3 have XOR 0. What is true for the player to move?

   They win by taking 1 stone from the pile of 1.They lose, because every legal move makes the XOR nonzero.They win, because the pile of 3 is the largest.The result depends on who moved first in the game.
2. 2. What is the XOR of the piles 6, 7 and 9?

   Type a number.

3. 3. Match each term to its meaning.

   Choose the matching item for each row.

   P-positionChoose…1 for each bit where the two inputs differthe player to move losesthe player to move winsN-positionChoose…1 for each bit where the two inputs differthe player to move losesthe player to move winsXOR (^)Choose…1 for each bit where the two inputs differthe player to move losesthe player to move wins
4. 4. Put the steps for finding a winning Nim move in order.

   Use the arrows to put the steps in order.

   1. 1.Find the highest set bit of that XOR.↑↓
   2. 2.Set the new size of that pile to the pile XOR the total.↑↓
   3. 3.Pick a pile that has that bit set.↑↓
   4. 4.Compute the XOR of all pile sizes.↑↓
   5. 5.Take the stones that leave that pile at its new size.↑↓
5. 5. Piles 3, 4 and 5 have XOR 2. Which statements about the winning move are true?

   Pick every answer that is true.

   It takes 2 stones from the pile of 3.It is the only winning move.It takes 2 stones from the pile of 4.After it, the piles are 1, 4 and 5, with XOR 0.