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sticks

 
 
Reply Thu 11 Nov, 2004 03:23 am
Deleted because puzzle is used in contest




Whim
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Type: Discussion • Score: 1 • Views: 665 • Replies: 8
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markr
 
  1  
Reply Thu 11 Nov, 2004 03:51 pm
48, 52, 80, 84

Method: Some insight into how the sticks are likely to be arranged and a spreadsheet. I don't know if this solution is unique.
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whimsical
 
  1  
Reply Fri 12 Nov, 2004 02:45 am
Smile

whim
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whimsical
 
  1  
Reply Sun 14 Nov, 2004 09:49 am
Can you get an unique answer if you know the sticks are eating-sticks . 80 cm is a bit long for such an eating tool.



whim
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whimsical
 
  1  
Reply Sun 14 Nov, 2004 09:52 am
oops double post


whim
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markr
 
  1  
Reply Sun 14 Nov, 2004 11:31 am
You get close, but not exact, with a triangle that has sides 20, 19, and 16. The height (with 19 as the base) is 14.9462. There are four different triangles you can form with three of the chopsticks. Each of the triangles has three heights since there are three choices for a base. Here are the numbers for 15, 16, 19, 20:
Code:
Sides Heights (ordered to match bases)
20 19 16 14.1989 14.9462 17.7487
20 19 15 13.4700 14.1789 17.9600
20 16 15 11.8279 14.7849 15.7705
19 16 15 12.2305 14.5237 15.4919

Here's a useful formula for the area of a triangle given sides of length A, B, C:
S = (A+B+C)/2 (semi-perimeter)
Area = sqrt(S * (S-A) * (S-B) * (S-C))

To calculate the three heights of a triangle, calculate the area, and multiply it by 2 (area*2). Then, for each side (base), divide the area*2 by the length of the side. That is the height.
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whimsical
 
  1  
Reply Mon 15 Nov, 2004 11:58 am
What values do work?
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markr
 
  1  
Reply Mon 15 Nov, 2004 08:41 pm
Whim,

Here are all the solutions for a relaxed set of conditions. Here, the only requirements are that all chopsticks are different lengths less than 50cm. It appears that 30, 28, 26, 24 is the smallest solution to your problem.

One issue: Does "but his two sticks are longer than yours" mean that both of his are longer than both of yours? If so, this is not a solution. You have to go to 60, 56, 52, 48 to satisfy that condition. I can send you a longer list if you wish.

3 24 25 26
4 12 13 15
6 20 25 29
7 12 15 20
8 9 10 17
8 10 17 21
8 21 29 35
8 24 26 30
9 15 28 41
11 12 13 20
11 24 25 30
12 13 14 15
12 13 20 21
12 13 30 37
12 13 37 40
12 15 17 25
12 15 20 25
12 15 26 37
12 15 37 44
12 19 20 37
12 36 39 45
14 24 30 40
15 16 25 39
15 17 25 28
15 17 28 39
15 17 39 44
16 18 20 34
16 20 34 42
17 24 25 26
20 25 29 36
21 29 35 48
22 24 26 40
24 25 39 40
24 26 28 30
24 26 40 42
36 39 42 45
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whimsical
 
  1  
Reply Tue 16 Nov, 2004 01:29 pm
Thanks mark



Whim
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