Sticks
Probability
Level
3
You have 10 sticks with lengths 1,2,3......,9,10. How many triangles can be formed taken. 3 sticks at a time.
121
50
120
122
69
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Impossible with shortest side 1.
Shortest side 2 : 1 × 7 = 7 ways
Shortest side 3 : 2 × 5 + 1 × 1 = 11 ways
Shortest side 4 : 3 × 3 + 2 × 1 + 1 × 1 = 12 ways
Shortest side 5 : 4 × 1 + 3 × 1 + 2 × 1 + 1 × 1 = 10 ways
Shortest side 6 : 3 × 1 + 2 × 1 + 1 × 1 = 6 ways
Shortest side 7 : 2 × 1 + 1 × 1 = 3 ways
Shortest side 8 : 1 × 1 = 1 ways
Total number of triangles
= 0 + 7 + 11 + 12 + 10 + 6 + 3 + 1
= 50