A number consisting of 2 identical digits, say
xx is multiplied by
99.
Write down the product P, given its tens digit (i.e. 3rd from the left) is y.
P&P only.
xx*99=(10x+x)*(1001)=1000x+100x10xx=xx00xx
xx00  xx = (x, x1, 10(x+1), 10x)
If 10(x+1)=y => 10x=y+1; x1=8y; x=9y
P= (9y,8y,y,y+1)
Verifying:
99*77: x=7: y=10(x+1)=2
P= (92, 82, 2, 2+1) = 7623
Edited on February 26, 2018, 8:42 am

Posted by armando
on 20180226 08:41:13 