Pick-Up Sticks
Alice and Bob are playing a game in which they take turns removing 1, 2 or 3 sticks from a pile of sticks. The game is won by the person who removes the last stick(s). If the number of sticks in the pile is denoted by a natural number n , what number must n be a multiple of for Bob to beat Alice without fail if Alice goes first?
The answer is 4.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
If n is a multiple of 4 then Bob takes 4-k sticks when Alices takes k sticks. 0 is also multiple of 4 so he takes the last stick.