## Math Forum - Problem of the Week

### Fractris

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Fractris

In the Fractris game, you will be trying to finish as many rows as possible using different combinations of fractions. The computer will start you off with a random fraction and then it will be up to you to add your fractions to fill up the row exactly to score points. You will gain more points if you can avoid using the same fraction twice.

To start playing, click on the Run button. You will see a block fall immediately on the left of the grid. To add to that block, select a fraction on the right side by clicking on it. You should then see a block fall into place. Keep adding blocks until you have filled the row. If you fill your row up without using any fraction more than once, it will disappear so you can start a new row. Otherwise, your row will remain and you will start on the next row up. You'll have 250 seconds to finish as many rows as possible!

To play the game again, press the Reset button, then press the Run button.

### Questions

1. If the computer sends down a 1/3 block, how can you finish the row with the fewest number of blocks and without using the same size block twice?

2. If the computer sent down 1/5, would you be able to fill the row? If so, how could you do it with the fewest blocks? If not, explain why not and tell how close you could get to completing the row.

3. What do all the fractions in the Fractris game (1/2, 1/3, 1/4, 1/6, 1/12, 5/12) have in common?

Bonus: What are all the different combinations of the fractions 1/2, 1/3, 1/4, 1/6. 1/12, and 5/12 that will sum to 1 without using any fraction twice? Explain how you know that you have found all the ways.

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