Math Puzzle: a Numbers Game
Posted on August 16, 2008
Filed Under Math Puzzles |
Last week’s puzzle was solved a bit too easily, so it’s take 2 for me this week with yet another math puzzle - more of a logic puzzle really.
Imagine the following game played between myself and yourself:
1. The game is carried out in turns.
2. The first person to call out 50 wins.
3. Each turn, each player calls out an integer.
4. The starting player must name an integer between 1-10 (1 and 10 included).
5. The next player must add an integer between 1-10 to the initial number.
For example: I say, “5″, you say “14″, I say “23″, you say “24″, I say “34″, you say “44″, I say “50″ and win.
I give you the choice of who goes first. What will you choose, and what is the optimal strategy?
Good luck, and don’t hustle people in pubs with this :).
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2 Responses to “Math Puzzle: a Numbers Game”
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I actually got this question for an interview once. I would go first. The optimal strategy is to start with 6 and for each turn, to increase the number you stated by 11. So, your numbers would be: 6, 17, 28, 39, 50.
A good way to think about it is recursively, starting from 50. I want my opponent to pick anywhere between 40 and 49. In order to limit his or her choice to these numbers, I would have to pick 39. In order to pick 39, I want my opponent to pick anywhere between 29 and 38. So, I would have to choose 28. Etc…
Yep, that’s as good an answer as I could’ve hoped to give! A friend of mine got this on one of HIS interviews once, so I guess the readers here should watch out for this popular little piece ;).