Triangular Number 66

66 = 1 + 2 + 3 + … + 11 is the 11th triangular number. The formula 1 + 2 + … + n = n(n+1)/2 was famously rediscovered by the 10-year-old Gauss when his teacher assigned the sum of numbers 1 to 100 as busywork, expecting it to keep pupils quiet. Gauss paired 1+100, 2+99, 3+98, and saw 50 pairs each summing to 101: answer 5050. He handed it in seconds later. The triangular numbers appear everywhere — in Pascal's triangle, in combinatorics (the number of handshakes in a group), and as the differences of perfect squares.