The game of 100 It is a simple game that It can be played everywherejust have a mind and opponent! It works like this: it is said alternately a number each and the first one who manages to say the number 100, wins. Clearly, there are rules that establish at each turn what numbers can be said by the two opponents: each number must be strictly greater than the previous one, but not too much bigger!
This said, it seems an almost random game, but those who know the strategies are unbeatable! Let’s see the rules of the game and we use the mathematics of the sums to discover the winning strategy with which all games can be won.
The rules of the game of the 100: what numbers can be said
The game of 100 is a mathematical game and foresees Two players That, in turnsay a number between 1 and 100 according to the following rules:
- To leave, The first player say a number between 1 and 10;
- at each turnthe player must say a largest number of the previous onebut can exceed the last issue played by the opponent at a maximum of 10;
- wins the first player who manages to say the number 100.
Let’s do a example To understand how the rules work:
- Player A: 3
As per rules, the first player has chosen a number between 1 and 10 - Player B: 11
The second player has chosen a second number larger than 3, but which does not exceed 10 (for example, he could not have said 14) - Player A: 14
The ball returns to the first player, who continues according to the rules - Player B: 24
The game continues according to the rules, up to the number of number 100 - …
- Player A: 95
At this point, the player A knows he has lost, because B according to the rules, he can say 100 - Player B: 100
… and in fact it does it! B is the winner
As you see the rules are easy, but what will be the best strategies? We explain one of the winning strategies.
The strategy to win all the games at the game of 100
The Cento gameis a Fixed game Just like the trio. Being a solved game means that all possible results are known and therefore if we follow a precise strategy,we are sure of the outcome who will have the game. In the trio, however, we know that if we follow a precise strategy, we never lose! But there is no strategy to always win. In the game of the 100 instead, there is a strategy that will allow us to win all games As long as you are starting. But let’s take one step at a time and understand the strategy with an example.
Let’s imagine that towards the end of a game the player say the number 89At this point he won the game because player B can only choose between numbers 90, 91, 92, 93, 94, 95, 96, 97, 97, 99 that all 10, or less, from 100. If for example B chose 90, to the player a add 10 and play 100 for win the game.
The core of the matter is that 89 is the perfect number to win, and therefore the strategy is being able to get to this number, because it is exactly 11 from 100 and any number chooses the opponent, following the rules of the game, it cannot be 100 but it will distance from 100 less than 10, so at that point the player A with a single move can be reached in one hundred and winning.
Well, if we can play 89 we won, but how do we prevent our opponent who play 89? Just be able to play the number 78 Which is exactly 11 from 89: for the same motivations as before, if we come to play the number 78 our opponent will not be able to prevent us from playing 89 and therefore win the game by playing the final 100. And how do we be sure we can play 78? We begin to have guessed the strategy.
The trick is to return backwards 11 numbers at a time To find all the numbers that can make us win the game: 100, 89, 78, 67, 56, 45, 34, 23, 12, 1. It is an easy number sequence to remember because it contains all the numbers, between 1 and 100, in which the figure of the units exceeds one the figure of the dozens. If during the game we can play any number of this sequence we are in an iron barrel and our opponent – unless the strategy knows in turn! – He cannot prevent us from playing the subsequent numbers of the sequence up to 100 and win the game.
Having understood the example, we can formulate the best strategy for this game:
- start first by playing number 1 and subsequently follow all the numbers of the Winning sequence 1, 12, 23, 34, 45, 56, 67, 78, 89, 100
- Or start for seconds and try to enter as soon as possible in the sequence of winning numbers. In this case the victory is certain only if your opponent does not know this strategy, otherwise the defeat is certain!
As you can see, this game is very simple and you need nothing but our mind and an opponent! But if after a while you get bored, know that you can invent an infinite number of variants of the same game, simply by changing the number of arrival and the rules that establish which numbers can be said or not.
For example there are the Zero game and the game of 25. The first of the two – the Zero game – it is the same as game of 100just go back! It starts by choosing a number between 90 and 99 and continues by subtracting from time to time to the maximum 10. The first that reaches 0 wins. In the game of 25 Instead, we start by choosing a number from 1 to 5, you climb from time to time to a maximum of 5 and you win the first one who says 25. Also for these two games there are winning strategies similar to those we have told you, but with some small differences that we challenge you to find.
