Sum of digits

Algebra Level 2

What is the sum of the digits of $(1010101)^2 =?$

Hint: We can calculate the above product without using a calculator. Also we can use modular to find the sum of the digits.

18 20 19 16 17

1 solution

Kenny O.
Oct 14, 2017

$1010101^2$ =1020304030201. The sum of its digits is 1+2+3+4+3+2+1=16.

Thank you.

Hana Wehbi - 3 years, 7 months ago

$(1010101)^2 = (1010101)\times(1010101) = 4×4 = 16$ .

Note : sum of digits of $1010101$ is $4$ .

Naren Bhandari - 3 years, 7 months ago

That is also a nice way of solving it.

Hana Wehbi - 3 years, 7 months ago

This does not work for all integers. E.g.
15X15=225 sum of digits=9. However (1+5)(1+5)=36

Kenny O. - 3 years, 7 months ago

he didn't mean in general, only for this problem.

Hana Wehbi - 3 years, 7 months ago

@Hana Wehbi – Sorry, Mam , I'm a boy. :) :)

Naren Bhandari - 3 years, 7 months ago

@Naren Bhandari – Ok, l will edit it, good you told me.

Hana Wehbi - 3 years, 7 months ago