This program uses a brute force approach to solve the 

birthday problem, which asks for the number of people that must

be in a room so that it's more likely than not that at least

two of the people share a birthday, in this case assuming 365 

days in a year and a uniform distribution of birthdays througout the year.

​

The code is intended to be easily understood from

basic mathematical notions and programming concepts, and for 

the problem above with a shared birthday probability > 1 / 2, 

this code is sufficient. However, it may hit computational 

limits if this threshold probability of 1 / 2

is replaced with 0.9999999999 or greater; in that case,

it may give incorrect results.

​

NOTE:

We could also compute p as

1 - (product from k = 0 to n - 1 of (1 - k / 365)).

*/

​

//r^(k falling) = r * (r-1) * ... * (r - (k-1))

function falling(r, k) {

  let power = 1;

  for (let i = 0; i < k; i++) {

    power *= r - i;

  }

  return power;

}

​

let p; //probability of a collision

let pThreshold = 0.5; //threshold probability

let n = 1; //number of people

​

do {

  p = 1 - falling(365, n) / 365 ** n;

  console.log(`n = ${n}: ${p}`);

  n++;  

} while (p <= pThreshold)