Can you solve my primary school math brain teaser?
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When I was clearing my old textbooks in my old house, I found a piece of primary school optional exercise with a math brain teaser. I tried to solve it. Here is the question:
Sam is coming to play a game with Ana. Sam wrote a series of numbers on the board: “1, 2, 3, 4 …… 53, 54, 55”.
Sam said to Ana, “There are 55 numbers from 1 to 55.
We will take turns to cross out three consecutive numbers,
for example, 10, 11, 12. If one of us does not have three consecutive numbers to cross off, that person loses.
A crossed-out number cannot be crossed out again.
And since I suggested this game, you can be the first to cross it off.”
In order to maximize her chances of winning, which three consecutive numbers should Ana cross first?
Give it a try being scrolling down for the solution.
Solution:
Ana first crossed out the middle numbers, that is, 27, 28 and 29, and then the numbers were divided into two groups, left and right, each with 26 digits.
The numbers are divided into left and right groups, each with 26 numbers.
Then it’s Sam’s turn. Wherever Sam crosses, Ana crosses out the numbers in the other group in the same relative position as Sam.
For example, if Sam crosses 1, 2, 3, Ana will cross off 30, 31, 32.
This ensures that Ana will have numbers to cross out before Sam runs out of numbers to cross out.
This ensures that Ana will have numbers to cross off before Sam runs out of numbers to cross off.
Therefore the person who crosses first will not lose.
Did you get it right?
