The Number Rainbow - 12/04/2013

[showmyiq]

Which number is not like the others in this number rainbow?
Why?

15
28
45
56
78
91

[Gusto]

78

[showmyiq]

Can you please explain how did you reach that answer?

[showmyiq]

Since I didn’t received an explanation of that answer I highlighted as incorrect.
The correct answer is 56 and it was successfully solved by Sergey Sokolov via facebook.

The pattern here is adding all the numbers up to N. This are called the triangular numbers and I have already published a sections with them.

1
1+2 = 3
1+2+3 = 6
1+2+3+4 = 10
1+2+3+4+5 = 15
1+2+3+4+5+6 = 21
1+2+3+4+5+6+7 = 28
1+2+3+4+5+6+7+8 = 36
1+2+3+4+5+6+7+8+9=45
1+2+3+4+5+6+7+8+9+10=55
1+2+3+4+5+6+7+8+9+10+11=66
1+2+3+4+5+6+7+8+9+10+11+12=78
1+2+3+4+5+6+7+8+9+10+11+12+13=91

Therefore 56 is the wrong number in this number set! It’s not triangular number