9 Three Idols 
5 

Betsy and Patsy 
11 

Measuring Up 
9 

Three Idols 
11 

Gold or silver? 
1 

Classic Knights & Knaves 
3 

Ball Drop 
1 

Parodoxical Statements from Life 
4 

Guilty Innocence 
The doublesquare number problem
Yeah I suppose I have to agree with you that a mathematical model is definitely nicer! context 
Products Algorithm
I like the solution, indeed interesting, I hadn't seen this one yet. yuktijain: the solution you give is an O(N^2) solution which is the trivial solution that this puzzle wants us to improve. context 
The doublesquare number problem
Brute force programmatic solution in Python: from math import pow [n for n in range(1000,10000) if pow(n/100,2)+pow(n%100,2)==n] context 