A young listener (or really her father, on behalf of a young listener) wrote us:
Two players each choose any 10 digits from 1 to 36.
Then you take turns
rolling 2 die with the object being trying to be the first to eliminate all
your numbers. You can eliminate any of your numbers by matching it with either
the number on one/both of the die or using the sum or product of the die.
If I chose 1, 2, 3, 4, 5, 6, 7,8, 9, 10. Then if I roll a 2 and a 4 I can
eliminate the 2 & 4, the 6 OR the 8. The other player also eliminates from his
list using your roll.
What is the best 10 numbers to choose?
Thanks for a great puzzle Anika!
Well let’s see:
The first, fairly straightforward task is to work out the probabilities that various numbers will be eliminated on a given roll. (And only 20 numbers out of the 36 can be eliminated at all!)
Some interesting variations: a given roll can eliminate multiple numbers; this is perhaps more subtle since you want to find sets of numbers that could perhaps be wiped out efficiently, and at a high probability.
An additional possibility would be to allow, say, a roll of 2 & 4 to wipe out 24. This rule would allow 30 different numbers to be eliminated.
We gave two puzzles this week; I’m going to move discussion of the second one to the next thread.