The Parentheses Problem

                                                                                                     by Rina Ono

                                                                                                              October 16,2014        Period 8

This project is about find a different answer in the subtraction problem and find a pattern of the problem.

8-4-2-1

8-4-2-1=1

(8-4)-(2-1)=3

8-(4-2)-1=5

8-(4-2-1)=7

16-8-4-2-1

16-8-4-2-1=1

16-8-4-(2-1) =3

16-8-(4-2)-1=5

16-8-(4-2-1) =7

16-(8-4)-2-1=9

16-(8-4)-(2-1) =11

16-(8-4-2)-1=13

16-(8-4-2-1) =15

Predict: 16

I predicted 16 because, 8-4-2-1 and 16-8-4-2-1 answer only has odd number and the answer is until the 1 less number then the biggest number. For example if its 8-4-2-1 then the biggest answer is 7 and 1 less number of 8 is 7. It is the same things with 32 and 16 then I counted the odd number until 31 then there are 16. I also think that its 16 because the number of the answer is the second number of the question. For example the 8-4-2-1 answer I think is 4 answers and the second number is 8-4-2-1. I think also the answer is  twice time more each time.

Conclusion

I think the most interesting pattern is that the number of the answer is second number of question if its times two all the time. The another things I think its interesting is that if I place parentheses same place it is same answer for example 8-4-(2-1)=3 and 16-8-4-(2-1)=3 it is same things with 1, 5 and 7.  

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