# Study the number patterns and fill in the missing number

This problem seems easy but I have been working on it for quite some time with little clue. It is about finding number patterns, I have tried many different ways, which seem to work at first but fail later.

I tried:
1. The multiplicative and additive pattern when we go around the triangle clockwise and anticlockwise, but it didn't seem to work.
2. I tried to find the difference between the number on an angle and the opposite side, it seemed to work for the first two triangle:
for the leftmost picture, 2/3-1/4=1/2-1/12=3/4-1/3=5/12.
for the middle picture, 3/10-1/10=1-4/5=3/5-2/5=1/5.
but for the rightmost picture, 11/20-1/3=13/60, 3/4-7/15=17/60.
3. I also tried:
for the leftmost picture 1/3-1/4=3/4-2/3=1/12, 1/4-1/12=2/3-1/2=1/6, 1/3-1/12=3/4-1/2=1/4
similar for middle picture,
but it does not work for the rightmost one.
4. I have also observed that the first picture is a square while the second and the third is a triangle, I tried to square and cube some numbers but couldn't find any clue.
5. I also tried to look for some patterns between the pictures instead of within the pictures but could find any clue as well.

Is it because I am not sensitive enough with numbers or for some other reasons? Could anyone help sharing some insights?

Many many thanks!

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My guess would have been that the sum of numbers on each edge is 1.5, but this doesn't work for 1 edge on the rightmost triangle. In any case, my guess is $\frac{5}{12}$. – Calvin Lin Oct 12 '13 at 14:40