Something special about the number 36

special-number-36.md

I just turned age 36 (by Korean standards) and noticed that some of my friends seem to be sad to have such a "big" number as their age.

So I thought about whether there could be anything special about the number 36 and I found a simple and interesting pattern for that number.

When you divide 36 by 2, the answer is 18 (36 / 2 == 18); and when you multiply each digit of 36 individually, the answer is also 18 (3 * 6 == 18)!

So it seemed kind of special to me and then I wondered if there is any natural number that has these same features (except 0)

As a non-math person, the shocking discovery was that 36 seems to be the only number under 10M.

function digits(n) { 
  if (n < 10) { 
    return [n] 
  }
  
  return digits(parseInt(n / 10))
    .concat(n % 10) 
}

assert(JSON.stringify([7, 8, 9, 4, 5, 6]) === JSON.stringify(digits(789456)))
// test digits function

function findThatNumber(rangeTo){
  return [...Array(rangeTo).keys()]
    .map((n) => [n / 2, digits(n).reduce((x, y) => x * y, 1)])
    .filter(([x, y]) => x == y)
    .map(([x]) => x * 2)
}

findThatNumber(100)
// [ 0, 36 ]
findThatNumber(1000)
// [ 0, 36 ]
findThatNumber(10000)
// [ 0, 36 ]
findThatNumber(100000)
// [ 0, 36 ]
findThatNumber(1000000)
// [ 0, 36 ]
findThatNumber(10000000)
// [ 0, 36 ]

The last one took 40 seconds on my Mac Mini so I stopped there for now.

Maybe I will keep discovering more special things about the number 36 from now on.