January 2020 : Solution

Nate (the first player) can always win in this game, by starting with the number 3. After this first turn, Nate can force the running total to increment by units of 12. This could happen 2 different ways:

  1. If Alter picks some number X between 2 and 10, Nate chooses 12-X
  2. If Alter picks 1, Nate responds by picking 1 as well. Now Alter cannot pick 10 (since this would force the sum of the previous two numbers to be 11), and must pick some other number Y. Nate then picks 10-Y.

In this way, Nate can force Alter to choose numbers when the running total is equal to 3, 15, 27, 39, 51, 63, 75, 87, and 99. At this point, Alter is forced to take the total to 100 or greater.

Congratulations to everyone who solved this month’s puzzle!