All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > General
FIGURE it out ! (Posted on 2004-09-10) Difficulty: 4 of 5
  1. With an unlimited supply of toothpicks of n different colors, how many different triangles can be formed on a flat surface, using three toothpicks for the sides of each triangle?
    (Reflections are considered different, but rotations are not.)

  2. How many different squares?

No Solution Yet Submitted by SilverKnight    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution -- numbers | Comment 7 of 12 |
(In reply to solution by Charlie)

For squares, following the formula I gave, the following table breaks down the possibilities:

 n   4-col  3-col  2-col  1-col  total
 1      0      0      0      1      1
 2      0      0      4      2      6
 3      0      9     12      3     24
 4      6     36     24      4     70
 5     30     90     40      5    165
 6     90    180     60      6    336
 7    210    315     84      7    616
 8    420    504    112      8   1044
 9    756    756    144      9   1665
10   1260   1080    180     10   2530
11   1980   1485    220     11   3696
12   2970   1980    264     12   5226
13   4290   2574    312     13   7189
14   6006   3276    364     14   9660
15   8190   4095    420     15  12720
16  10920   5040    480     16  16456
17  14280   6120    544     17  20961
18  18360   7344    612     18  26334
19  23256   8721    684     19  32680
20  29070  10260    760     20  40110

  Posted by Charlie on 2004-09-10 16:55:57
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information