The Fruit Game is a fun game to play with your friends, and you don't even need fruit to do it. Just take any small object, like paper clips, marbles, or pennies--and make the piles.
Then you take turns removing the objects from the piles. You can take as many as you like, but you must take at least one, and you must take from only one pile. The person to take the last object is the winner.
Test your understanding | |
It's your move. There are 5 bananas, and 1 orange. What do you do? |
Therefore, when it's your move, you want to try to change the table so that it is one of the winning positions. If you can change the table so that your opponent is faced with 1-1, you will surely win.
For example, suppose its your move and and you there are 2 oranges and 1 banana. You could win the game by removing 1 orange, thereby creating the winning 1-1 position.
For the rest of this page, we will refer to positions with numbers like 3-2-1 or 7-6-5-4. These numbers tell you how many fruit are on the table. E.g., 3-2-1 means 3 of one fruit, 2 of another, and 1 of another. When it's your turn, you try to take away fruit so that the result is a winning position.
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It's your move. There are 5 bananas, and 6 oranges. What do you do? |
Of course, any time your opponent takes all of one of the two piles, you simply take all of the other pile and immediately win the game, since the object of the game is to take the last fruit from the table.
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It's your move. There are 3 bananas, 3 oranges, 3 lemons, and 4 peaches. What do you do? |
You can play the table as if there are two different games going on at the same time. E.g., if your opponent changes one of the piles with 5 fruit in it, change the other 5 fruit pile so that it is equal.
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It's your move. There are 7 lemons, and 2 oranges, and 3 peaches. What do you do? |
Consider if it was your move and you were looking at 1 orange, 2 bananas, and 3 lemons. No matter what you do, your opponent will be able to turn the table into 1-1, or 2-2, or some other winning position. For example, if you decide to take one of the lemons (leaving 1-2-2) your opponent would simply take away the one orange to show you 2-2. And as we discussed above, that is bad. Very bad.
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It's your move. There are 7 lemons, 6 oranges, and 5 peaches. Name three winning moves that you could make. |
Winning positions are: 5-4-1 6-4-2 6-5-3 7-4-3 7-5-2 7-6-1
Other than 3-2-1 discussed above, these are the only three-pile winning positions. Notice that 7-5-2 is exactly how the "Original Fruit Game" was set up, and since the player was forced to go first, there was no way to win. Stinkers, aren't we?
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4-3-2-1 is not a winning position. Why not? |
We can start off with two easy ones that you should never forget, the "four number runs." These are 5-4-3-2 and 7-6-5-4 -- each pile smaller than the one before it. No matter what move your opponent makes with these winning positions, you'll be able to turn it into another winning position easily.
Test your understanding | |
When the Fruit Game starts, you see 7 lemons, 6 peaches, 3 lemons, and 2 bananas. Do you want to go first? |
Without any further ado, here they are: 6-4-3-1 6-5-2-1 7-4-2-1 7-5-3-1 7-6-3-2
I start the game, and here is what's on the table:
This is a 7-6-3-2 position. From the section above, we see that this is a winning combination. It asks me, "Would you like to go first?" What do you think I should say?
Well, since the object of each move is to turn the table into a winning position, the correct answer is to click on No and let the Fruitmaster move.
The Fruitmaster says "I greedily gobble one banana." This leaves us with 7-6-3-1. Now we have to ask ourself, what is the move which turns this position into another winning position? There is no room for mistakes--it is critical that we turn the table into a winning position.
Fortunately, there are at least two things you could do. One thing is to "gobble" a peach leaving 7-5-3-1 -- another winning position. (See the Advanced Position above.) But far more direct would be to simply remove all 3 of the lemons, leaving the Fruitmaster with 7-6-1 -- a winning combination. That's what I'll do. (I click on the lemon on the far left, which removes all the lemons.)
Now he says, Aha! I simply snatch one banana! am looking at 7 oranges and 6 peaches, or 7-6. Do you see what to do? Yes, you can create a double by removing one orange, leaving him with 6-6.
He responds with I cleverly gobble one orange. So I eat a peach. Then he eats an orange, and I eat another peach. He continues to each the oranges one by one until finally he is faced with 1-1.
He eats the last orange, and I see the screen with only one little peach in the middle. I click on it, and go to the special "Winners' Page" where I am treated to a full-sized picture of the Fruitmaster himself.
Think your ready to try out what you've learned? Click here!
Test Your Understanding - Answers.
It's your move. There are 5 bananas, and 1 orange. What do you do? Remove 4 bananas. It's your move. There are 5 bananas, and 6 oranges. What do you do? Remove 1 orange. There are 3 bananas, 3 oranges, 3 lemons, and 4 peaches. What do you do? Remove 1 peach. There are 7 lemons, and 2 oranges, and 3 peaches. What do you do? Remove 6 lemons. There are 7 lemons, 6 oranges, and 5 peaches. Name three winning moves that you could make. Remove 4 lemons, or 4 oranges, or 4 peaches. 4-3-2-1 is not a winning position. Why not? Because you can remove 4 fruit to make 3-2-1. 7 lemons, 6 peaches, 3 lemons, and 2 bananas. Do you want to go first? No. |