Singmaster’s Conjecture (opens in new tab)

In Pascal’s triangle, each number is the sum of the two above it. Obviously, the infinite pyramid contains an infinite number of 1s, but most numbers appear surprisingly seldom: 2 appears just once. 3, 4, 5, and all odd primes appear exactly twice. 6 appears three times. Infinitely many numbers appear exactly six times, but we don’t know whether any appear exactly five or seven times. 3003 appears eight times, possibly the only such specimen. In 1971, Berkeley mathematician David Singmaster s...