Difference between revisions of "2005 PMWC Problems/Problem T10"

(Solutions)
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== Solutions ==
 
== 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.
 
 
[Comment: In this solution the number 837319737131 has many non-distinct two digit subsequences of prime numbers for example 37, 31, 73 all appear more than once. But the question asks for distinct two digit prime numbers.]
 
 
 
'''Second Solution:'''
 
  
 
We start with 97, which is the largest 2 digit prime.
 
We start with 97, which is the largest 2 digit prime.
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979373191713
 
979373191713
 
Which answer is correct?
 
  
 
== See also ==
 
== See also ==

Revision as of 09:00, 11 October 2007

Problem

Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number.

Solutions

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.

979373

And proceeding like this will get us

979373191713

See also

2005 PMWC (Problems)
Preceded by
Problem T9
Followed by
Last Question
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T: 1 2 3 4 5 6 7 8 9 10