Question

As my birthday approaches I start to collect leaves - a little bizarre perhaps, but I enjoy it! On the first day of the month I collect 1 leaf, on the second day I collect 2 leaves, the third day I collect 3 leaves, and so on. By my birthday I will have collected 276 leaves altogether. On which day of the month is my birthday?

Answer 1

let N represent the birth date, the date of the month.

so  1 + 2 + 3 + .... + N-1 + N  = 276
     This is an arithmetic series.  So  the total is given by
   N (N+1) /2  = 276
   N (N+1) = 2 * 3 * 23 * 2 * 2  = 23 * 24

 =>  the birth date is 23