Answer to question #10

10. You and I are to play a competitive game. We shall take it in turns to call out integers. The first person to call out “50” wins. The rules are as follows:
1. The player who starts must call out an integer between 1 and 10, inclusive;
2. A new number called out must exceed the most recent number called by at least one and by no more than 10.

Do you want to go first, and if so, what is your strategy?

Another little puzzle that I worked out for myself, I think it's right...

We'll call the players 'W' and 'L' (can you guess which one wins?) The trick is to start at the end and work backwards.

W wins if he says 50, he can say this if...
L says any number in the range 40 - 49 and will have to say one of these if...
W says 39, he can say this if...
L says any number in the range 29 - 38 and will have to say one of these if...
W says 28, he can say this if...
L says any number in the range 18 -27 and will have to say one of these if...
W says 17, he can say this if...
L says any number in the range 7 - 16 and will have to say one of these if...
W starts on 6.

So that is pretty much it W wins if he starts on 6 then simply follows the sequence 6, 17, 28, 39, 50. Another way of thinking about this is that W forces each pair of numbers to go up in 11's regardless of what L says, hence he starts on 6 which is 50 - 4x11.

 

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