Calculation of the year - solution

Wednesday, 20 March, 2019

This is the solution to the monthly maths problem from RTSdécouverte Calculation of the year

The sum of the digits of the number 102019 – 2019 is 18,160.

The number is too big simply to be “worked out” on a calculator. To get the solution, recall that 102019 is a 1 followed by 2019 zeroes.

A quick calculation (with or with calculator) shows that 10,000 – 2019 = 7,981. Further calculations give

      100,000 – 2019 = 97,981, 1,000,000 – 2019 = 997,981, 10,000,000 – 2019 = 9,997,981

Indeed the number 102019 – 2019 is of the form 999…9997,981 where the number of 9’s at the beginning is 2019 - 4 = 2015. Hence, the digits are 7,9,8,1 and an additional 2015 instances of 9 on the front.

Thus,            Sum of digits =  (2015 x 9) + 7 + 9 + 8 + 1 = 18,160.

 

 

You can read the original problem here: Calculation of the year