Difference between revisions of "2005 PMWC Problems/Problem T10"
I like pie (talk | contribs) (New page: == Problem == Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number. == Solution == {{solution}} == See also == {{PMWC box|year=200...) |
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== Solution == | == 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. | ||
== See also == | == See also == | ||
Revision as of 06:59, 9 October 2007
Problem
Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number.
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.
See also
| 2005 PMWC (Problems) | ||
| Preceded by Problem T9 |
Followed by Last Question | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
