Each of A, B, and C is a different zeroless pandigital number that satisfy this equation:

A*B=C²

Determine the minimum value of C.

That is a great compliment, Charlie; thank you.

Regarding algorithms, my first thought was to try every combination of 2 pandigitals, take the square root, and check.  I quickly saw one could just make a list of the squares and eliminate the square root step.  But still O(n^2) to check all the pandigital combinations.

Next, {tl;dr I ended up not doing this}  I thought about manipulating A and B so I could get the difference of 2 squares and then try to match the squares to a Pythagorean triple.  I had forgotten about Euclid's formula for generating Pythagorean triples, but rediscovered it.

Let mean = (a+b)/2  and diff = (a-b)/2  
(mean+diff)(mean-diff) = a * b = c^2
mean^2 - diff^2 = c^2
 mean is the midpoint between a and b, and
 diff is the distance from the mean to either a or b

Euclid's formula for generating a Pythagorean triple x^2 + y^2 = z^2
For positive integers m,n m>n
  x = m^2 - n^2 ... y = 2mn ... z = m^2 + n^2 of which x or y is pandigital

But I abandoned this quest and stopped working on it.  This was several days ago.

Then this morning after the problem posted, I just came up with the algorithm which ended up working.  I think sometimes the algorithm ideas have to churn around in the background before they gel into butter.

Posted by Larry on 2023-01-06 15:07:33