6 times
Probability
Level
3
What is the smallest number (different from 1) to appear 6 times in Pascal's triangle
Note: This problem is not original
The answer is 120.
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
This is just an outline of the proof; notice that 120 is the first and therefore smallest number to appear in the first, second and third diagonals. Hence by symmetry it occurs six times.
We can see that the subsequent diagonals have increasingly large numbers that quickly exceed 120, so by inspection no other numbers can occur six times and be lower than 120 as required.