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# Diamond Subtraction

11 replies to this topic

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Posted 10 May 2013 - 07:11 PM

Put four different whole numbers from 1 to 49, in the corners, then subtract the smaller from the larger and put the answers in between. Keep doing this until all four numbers become equal. How many steps can you make it last? The demo is "(14, 30, 18, 37) lasts 3 steps (don't count the step where they produce the same number)."  Find the longest lasting case.

DEMO:

stage 0

14  30           ---->           30-14

37-14     30-18

37  18                              37-18

stage 1

16                            16-13      16-12

13   12

19                           19-13      19-12

stage 2

3      4

6      7

stage 3

1

3        3

1

Stage 4 is stasis so it doesn't count

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### #2 bonanova

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Posted 10 May 2013 - 08:26 PM

Spoiler for Just to be sure

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #3 BobbyGo

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Posted 10 May 2013 - 08:38 PM   Best Answer

Spoiler for

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### #4 bonanova

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Posted 10 May 2013 - 09:09 PM

Spoiler for

Spoiler for Here is my count for your case

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #5 dark_magician_92

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Posted 10 May 2013 - 09:38 PM

Spoiler for

Can you share the code?

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### #6 BobbyGo

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Posted 10 May 2013 - 10:18 PM

Can you share the code?

I'm sure there are more elegant ways of coding this, and it only gives back the first longest set it finds (it won't return 8,21,45,1 after it finds 1,8,21,45) so I'm sure there is more than one answer.

Spoiler for code

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### #7 BobbyGo

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Posted 10 May 2013 - 10:49 PM

Just realized the section:

a1=sqrt ((a2-b2)*(a2-b2));

b1=sqrt ((c2-b2)*(c2-b2));

c1=sqrt ((c2-d2)*(c2-d2));

d1=sqrt ((a2-d2)*(a2-d2));

should actually be:

a1=sqrt ((a2-d2)*(a2-d2));

b1=sqrt ((a2-b2)*(a2-b2));

c1=sqrt ((c2-b2)*(c2-b2));

d1=sqrt ((c2-d2)*(c2-d2));

I don't think it really it effects the outcome, since it stayed in the same order.  But still.

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Posted 11 May 2013 - 12:46 AM

Spoiler for Just to be sure

yes, your example is 2 steps.

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Posted 11 May 2013 - 12:47 AM

Spoiler for Just to be sure

my example though shows 3 steps

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Posted 11 May 2013 - 12:56 AM

Spoiler for