Find eight 11-digit pandigital primes P<Q<R<S<T<U<V<W that can be written in a column so that each of the first 10 columns of digits has 8 distinct digits.
Find the set with smallest W.
Note:
(1) The eight pandigital primes are in base 10.
(2) Zeroes are allowed.
[Edit: this entire "solution" is incorrect, so please ignore; I missed the stipulation that they needed to be prime]
An 11 digit pandigital has one digit that appears twice. If 8 numbers start with a different first digit, the smallest that the largest number's first digit could be is 8.
The smallest 11 digit pandigital that starts with 8 is:
80012345679
So let this number be the top row: W = 80012345679.
Then let the next 7 rows be determined by subtracting one from the digit above (mod 10).
All 11 columns have distinct digits. Two columns are identical, but the statement of the problem did not prohibit this.
8 0 0 1 2 3 4 5 6 7 9
7 9 9 0 1 2 3 4 5 6 8
6 8 8 9 0 1 2 3 4 5 7
5 7 7 8 9 0 1 2 3 4 6
4 6 6 7 8 9 0 1 2 3 5
3 5 5 6 7 8 9 0 1 2 4
2 4 4 5 6 7 8 9 0 1 3
1 3 3 4 5 6 7 8 9 0 2
Edited on November 3, 2023, 10:24 am
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Posted by Larry
on 2023-11-02 12:15:11 |
Solution
