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Conquer the beginning of mathematical weekly diary
Mathematics in the game

One day, Sister Xixi played a game for us: two people counted from 1 to 10 in turn, and only counted to 1, 2 or 3 at a time. Whoever reports 10 first wins.

Everyone wants to "knock down" each other, but how can they win 100%? This question has been echoing in my mind, which makes me puzzled.

After returning home, I picked ten stones in a small basket for a novice to operate. I called my father and asked him to play this game with me. I found a pen and a notebook and recorded every step I did. The rule is this: my father and I take turns to take stones, up to three, and at least 1. Whoever gets the last one wins.

I lost the first game. It turned out that my father took it first, and my father made me lose "miserably" in the shortest time; I won the second game first, and I really won. ...

I read the record several times, and finally found that I added up the largest and smallest numbers: 1+3 = 4, and divided the total number of stones by the sum of the largest and smallest numbers, which is 10 ÷ 4 = 2...2. If there is a remainder, I will take it first, and the remainder is only a few stones. If there is no remainder, I will take it first. Now that the remainder is 2, I will take 2 stones, and the sum of the remaining stones and the opponent is a divisor of 3, so I can win.

In order to ensure the accuracy of the answer, I took 28 stones and played with my father again. With the above rules, I am invincible! ! !

It turns out that mathematics is everywhere in life, and they are waiting for you to discover!