My 4-year-old declares 36 the best number

My four-year-old son has declared 36 to be the best number. His reason: 36 is the only number (he knows of) that is both a square and a staircase number AND an up-and-down-staircase number. &ldquo;Staircase numbers&rdquo; are what he calls triangular numbers (numbers that are the sum of the first $n$ integers). This name comes from the blocks he has that can be arranged into a staircase. He also…