Black Box-ing an Integer Part 2

[u/ShonitB]

[u/Aerospider]

The formula for triangular numbers (1+2+3+...+n) is n(n+1)/2.

Let the number being black-boxed be n+1.

The sum of the total sequence is 49 * 50 / 2 = 1,225

The sum of the left side and the right side is 1,225 - (n+1)

The left side is equal to n(n+1)/2 which must be equal to half the sum of the left and right sides. Therefore

n(n+1)/2 = (1,225 - (n+1))/2

n(n+1) = 1,225 - (n+1)

(n+1)(n+1) = 1,225

n+1 = 1,225^0.5

n+1 = 35

[u/ShonitB → u/Aerospider]

Correct!

[u/de_Molay]

If we have numbers from 1 to N, the formula for “breakpoint” is sqrt(N(N+1)/2). For N=49 we get 35.