2005 PMWC Problems/Problem T10
Problem
Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number.
Solutions
First Solution:
We list all 2 digit primes:
11, 13, 17, 19
23, 29
31, 37
41, 43, 47
53, 59
61, 67
71, 73, 79
83, 89
97
Picking a 9 would get us:
97371311
So we pick an 8.
837319737131
That's the greatest.
Second Solution:
We start with 97, which is the largest 2 digit prime.
97
Then we add 9 to get 79, the largest 2 digit prime with tens digit 7.
979
Add 3 to get 93, the largest prime less than 97
9793
Now the largest two digit prime with tens digit 3 is 37. So we add a 7
97937
Now we add another 3 as 79 already exists.
97937
And proceeding like this will get us
979373191713
Which answer is correct?
See also
2005 PMWC (Problems) | ||
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