Hmmmmmm. Whats the best number and why? THANK YOU IN ADVANCE!

Question

Two players alternately name a number from 1, 2, 3, 4, 5. The first player to bring a combined total of all the numbers announced to 31 wins. What is the best number to announce if you go first? Why? Explain.

 

Answer 1

The average of the numbers 1 to 5 is 3.  So in any given set of n turns, the most likely total will be 3n.  10 average turns would get to 30. 

 

So if the player who goes first chooses 1, then the sum of the next 10 turns are most likely to be 30, and the overall total of the first 11 turns is most likely to be 31, the winning number.  Since the first player gets to take the odd numbered moves, then he would be the one to take the 11th move, and he would win.

 

So the best first choice is 1.

 

 

Answer 2

Hi Catherine,

 

You want to be in a position to force the other person to pick a number that will get the total to be greater than or equal to 26.  That way you will be able on your next selection pick a number that gets you to 31.

 

The number you should pick first is 1.  Then after the other person picks you pick a number that when added to their pick gets you to six.

 

so if they pick 4 you pick 2.

 

 

this will create the series 1,7,13,19,25,31. And it will always be you who gets to 31

 

 

Hope this helps