@Yoogottam Khandelwal
–
Very nice observation too! Indeed both unit digits are 5, is a special case of sum of unit digits is 10.
–
Calvin Lin
Staff
·
1 year, 10 months ago

Log in to reply

Good observation. Do you know why it works?
–
Calvin Lin
Staff
·
1 year, 10 months ago

## Comments

Sort by:

TopNewestThis also works with 2 digit numbers where tens digit is same and the sum of unit digits is 10.

for eg,

74

76=(78)_6*4=5624 – Yoogottam Khandelwal · 1 year, 10 months ago

Log in to reply

– Calvin Lin Staff · 1 year, 10 months ago

Very nice observation too! Indeed both unit digits are 5, is a special case of sum of unit digits is 10.Log in to reply

Good observation. Do you know why it works? – Calvin Lin Staff · 1 year, 10 months ago

Log in to reply

let the number be x5 where x is any number (1,2,3..9)

but, x5 is represented numerically as 10*x+5

now, when we square x5,

(10*x+5)^2

=(100*x^2)+(2 * 5 * 10 * x)+25

=(100 * x^2)+(100 * x)+25

=100(x^2+x)+25

=100 * x * (x+1)+25

so, the square of x5 is x * (x+1)_25 – Yoogottam Khandelwal · 1 year, 10 months ago

Log in to reply