Question 894058
Consider the ways that digits will give products of 27 and 14.
{{{3*9=27}}}, and {{{2*7=14}}}.
The units digits are 3 and 9, and the tens digits are 2 and 7; but we do not yet know
for sure which way they go in the two numbers.


There are no more than TWO combinations to check.
You want the product of the two numbers to be 2117.


{{{23*79=2117}}}?
No.
{{{23*79=1817}}}


{{{29*73-2117}}}?
Yes.
{{{29*73=2117}}}


<b>The two two-digit numbers are 29 and 73.</b>


I earlier tried the problem using variables and algebra but found an unresolvable system
of equations.