Problems & Puzzles: Puzzles

Puzzle 633. Palindromes & Pandigitals

The issue of detecting the palindromes that are product of pandigitals has been studied extensively in the always interesting pages of World!of Numbers  by my friend Patrick De Geest & his readers (see particularly the Plate 115).

As a matter of fact Frank Rubin, on January 2012, has produced one solution (and currently remains as the only known, as far as I know) but himself recognizes that this is neither the smallest nor the largest possible:

2067945831 x 2758436091 x 3581704962 = 20431106772402320427760113402

Here we ask specifically to find the smallest & the largest palindrome formed by the product of three pandigitals.

Q1. Get the smallest palindrome multiplying three ten-digits pandigitals (0 to 9)

Q2. Get the largest palindrome multiplying three ten-digits pandigitals (0 to 9)

Q3. Redo Q1 & Q2 for the nine-digits pandigitals (1 to 9)

Contributions came only from Giovanni Resta


Giovanni wrote:

My minimal (verified) solution for the 10-digits case is
1362840759 x 1082674593 x 1069458273 = 1577999653293663923569997751
My maximal (verified) solution for the 10-digits case is
9540138762x9568170243x9743625018 = 889414381197666666791183414988

while the two solutions for the 9-digits case are:
167538942 x 135278964 x 128576934 = 2914131213909093121314192 (verified)
923458167 x 982673514 x 983254671 = 892262201210191012102262298 (verified)



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