Problems & Puzzles: Puzzles

Puzzle 365. P*Q = R*S One more puzzle related to pandigitals before switching to other issues: Let P, Q, R & S to be zero-less pandigitals, such that: P*Q=R*S=Z Example: 234579618 * 234589176 = 351869427 * 156392784 Questions. 1. Find the minimal & maximal Z solution 2. Find the minimal & maximal Z solution if Z is "twice zero-less pandigital" 3. Redo 1 & 2 for pandigitals.

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Contributions came from Farideh Firoozbakht.

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Farideh wrote:

Q1.

The minimal Z solution is 15653859495417504 and
we have Z=123759648*126485973=123847956*126395784.

The maximal Z solution is 969335648653288752 and we have

Z=981763542*987341256=981564732*987541236

Q2.

Z = 786392845167493125 is the maximal twice zero-less pandigital solution.
And we have: Z = 817934625 * 961437285 = 879321645 * 894317625.

The minimal twice zero-less pandigital solution. Z = 112249549788637635  and we have:
Z = 142768593 * 786234195 = 157246839 * 713842965.

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