Both 36 and 42 are (2* a triangular number) and can be derived from either t=m*m+m or t=n*n-n iff n=m+1.
The second expression uses 3 digits only i.e. 6*6-6 or 7*7-7
and no addition.
To get an extra digit - replace one of the digits by
sqrt of its second power e.g. 6==>sqrt(6*6)
To get an extra k (k>1) digits - multiply the outcome of the generic 3-digits solution by 6/6 raised to a power kkkkkkk....k (concatenation of k-2 sixes). If k=2 ,the exponent is zero,
leaving just 6/6.
Of course ,the above method is applicable to 7 and to other digits.
I wonder, why the official solution requires different answers for 6 and 7.
BTW 66-6*6=30 unique for 6
Edited on December 15, 2009, 6:02 am