# Sunday Times Teaser 3085 – Lucky Progression

*by Victor Bryant*

#### Published Sunday November 07 2021 (link)

I wrote down a number which happened to be a multiple of my lucky number. Then I multiplied the written number by my lucky number to give a second number, which I also wrote down. Then I multiplied the second number by my lucky number again to give a third, which I also wrote down. Overall, the three numbers written down used each of the digits 0 to 9 exactly once.

What were the three numbers?

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Brute force:

Less brute force, more lines of code

Line 16 can be simplified to:

because line 12 eliminates all cases of total digit length > 10. Hence len(ss) must be <= 10. If each digit 0-9 is represented once and only once then total length of the three numbers must also be 10.

More complex but only 64 numbers are being checked on being pandigital.