Brain Teasers
Prime Directive
Arrange the numerals "11337799" to form an 8-digit number (referred to as "ABCDEFGH") that meets the following conditions:
1) ABCDEFGH is a prime number
2) HGFEDCBA (reversing the digits) is a prime number
3) all consecutive 2-digit subsets of ABCDEFGH are prime numbers (AB, BC, CD, DE, EF, FG, GH are all prime)
4) all consecutive 2-digit subsets of HGFEDCBA are prime numbers (HG, GF, FE, ED, DC, CB, BA are all prime)
1) ABCDEFGH is a prime number
2) HGFEDCBA (reversing the digits) is a prime number
3) all consecutive 2-digit subsets of ABCDEFGH are prime numbers (AB, BC, CD, DE, EF, FG, GH are all prime)
4) all consecutive 2-digit subsets of HGFEDCBA are prime numbers (HG, GF, FE, ED, DC, CB, BA are all prime)
Answer
97131379 (97, 71, 13, 31, 13, 37, 79) and its reverse 97313179 (97, 73, 31, 13, 31, 17, 79)The only available 2-digit prime numbers are: 11, 13, 17, 19, 31, 37, 71, 73, 79, and 97. The number pairs that are prime in both directions are: 11/11, 13/31, 17/71, 37/73, and 79/97 (19 is eliminated since its reverse, 91, is not prime). With these numbers, it can be seen that 9 can only be paired with 7. Therefore, the solution must be of the form 97????79, 9797????, or ????7979. ???? must therefore be 1313, 3131, or 3113. This leaves the possible solution pairs of 97131379/97313179, 97971313/31317979, 97973131/13137979, 97973113/31137979, and 97311379/97311379 (the last pair being a palindrome). Of these, only 97131379 and its reverse, 97313179, are prime numbers.
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Comments
what about 13799731?
The 99 in the middle of that one isn't prime.
Quite a nice teaser. It's a shame you need a primality tester to work out the answer though.
Jan 02, 2005
This problem was fun. I screwed up when I first worked it out because I had forgotten that 91 is NOT prime! I did get a hold of a primality tester though...I caught it in the end.
how about
17971373 / 37317971
how can i test?
17971373 / 37317971
how can i test?
This has 3 x 7s and only 1 x 9?
firstly, what's a primality tester, secondly, why is the palindromic number discarded? A and H are the same digit, it does not imply that ABCDEFGH and HGFEDCBA can NOT be the same number. I mean, I understand the point that mentioning its reverse is also prime would be redundant if it was palindromic, but 97311379 still meets ALL criteria, does it not?
Gah, I do believe I have seen my mistake, id 97311379 is not a prime number (not going to bother checking, I'll jsut accept that it is a composite number and call it a day).
This was a tough one!!! I almost got it, I thought I had it narrowed down to either 31137979, 13137979, or 31317979. I checked those all with a calculator and found that none of them were prime...so then I concluded that I was wrong or else it was some sort of trick. Thing is, I didn't think of putting BOTH 9's on the ends. I knew 9's had to be next to 7's, so I thought I was correct in making the string "7979" a mandatory inclusion. WRONG
EXCELLENT teaser!
EXCELLENT teaser!
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