Two players alternately pick integers from 1 to 10 until the sum reaches at least 100. The same number can be used more than once. The first person to reach at least 100 wins.
What is the Grundy number?
Start with the losing position with G-number 0 and then decide the other positions G-number.
You have a nim heap going up to the next $11k+1$. For example, playing anything else than $1$ from $88$ is losing, so the only value you can move to from $88$ is to $0$, so $88$ is $*1$. Then $87$ can move to $0, *1$, so it has value $*2$ and so on.