Parametrized general bimagic squares of order 6

Construct a parametrized family of general bimagic squares of order 6, extending the existing four-parameter family of pseudo-bimagic squares of that order.

Background

The paper constructs a four-parameter family of general pseudo-bimagic squares of order 6, but it does not construct a corresponding family in which the squared array also has equal diagonal sums. The authors state that they could not find such a family, while suggesting that one is likely to exist. This problem is therefore left unresolved for future investigation.

References

While we could not find a parametrized family of bimagic squares of order 6, since we have obtained a four-parameter family of pseudo-bimagic squares of order 6, it seems likely that a parametrized family of general bimagic squares of order 6 should exist.

— Construction of parametrized families of general pseudo-bimagic and bimagic squares  (2610.00915 - Choudhry, 1 Oct 2026) in Section 5, Concluding remarks