MATH GAME - EXPLAIN HOW TO GET ANSWER

Question

2 Player game 

goal is to reach 31

each player takes turns and chooses a number between 1-6 and adds it on

 

ex. P1 chooses 5 then P2 chose 6 so 11 P1 chose 2 so 13 goal is to reach 31 first

 

find out a strategy to win everytime and explain how u got this

Answer 1

You can solve this by working backwards:

 

1. If the goal is to get 31, then your goal should be to not get 25-30 on your previous turn (because your opponent could pick a number 1-6 from anything between 25-30 and win). You want your opponent to have to pick a number in this range. So your goal should be to end this turn at 24 since you would win 100% of the time from there.
2. So if 24 is the magic number for winning, we don't want to let our opponent get to it first. So the previous turn's goal should be to get to 17 because they would then have to pick a number 18-23 and you could then pick 24.
3. Following this pattern, to get to 17 you'd want to end the previous turn at 10.
4. Since this takes us to the beginning of the game, you would use one of two strategies depending on if you are picking first or second.
1. If picking first, then you want to start with 3. By starting at 3, your opponent must pick between 4-9 and then you can pick 10.
2. If picking second...
1. If your opponent chooses 4-6, then just round up to 10.
2. If your opponent chooses 1-2, then round up to 3 and then follow the previous strategy from there.
3. If your opponent chooses 3, then you lose (unless they screw up the strategy somewhere along the way).

 

Here is a sample game to show what I mean:

 

Me - 3

Opponent (1) - 4

Me (6) - 10

Opponent (6) - 16

Me (1) - 17

Opponent (3) - 20

Me (4) - 24

Opponent (2) - 26

Me (5) - 31

 

So the way to win is to by being the first to claim 3 and/or 10, and then making sure to add a combined total of 7 with your opponent's pick on each subsequent turn.