2
$\begingroup$

7 = 31674ZS

8 = 883011SO

9 = 166037352UR

10 = 434782608WP

11 = 31701296735IG

What would 12 be equal to in this same pattern?

Hint:

Open your calculator.

Another hint:

Use the trial and error method.

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13
  • 1
    $\begingroup$ Is there a specific knowledge that's required, or is it trivial/not necessary? In case the 'knowledge'-tag should be used, I mean. $\endgroup$ Jun 1 at 7:09
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    $\begingroup$ @Prim3numbah, no, I'd say it's not necessary. 3*rot13(V whfg znqr gur ynfg gjb) + 5*rot13( yrggref nf vs gurl pbhyq or zvfhaqrefgbbq vs haqrefgbbq fb, gb znxr gur chmmyr rira gevpxvre.) I've added 2 tags that I feel are relevant. $\endgroup$ Jun 1 at 8:54
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    $\begingroup$ Ive tried different ways to solve it. Like using exponents, factorials etc but no progress. $\endgroup$ Jun 5 at 9:35
  • 2
    $\begingroup$ 3*rot13 and 5*rot13 are uhh just rot13. Anyway, it seems like we're intended to rot13(pbzovar gur gjb yrggref cre yvar) somehow, but darned if I can figure out how that leads to anything meaningful. $\endgroup$
    – Ed Murphy
    Jun 6 at 15:09
  • 1
    $\begingroup$ I think you may be overestimating how obvious your hints are. Feel free to answer any/all of these: Does this use A=1 B=2 etc. in some fashion? Does this involve anything more complex than addition, subtraction, multiplication, division, shifting decimal places, and/or concatenation? $\endgroup$
    – Ed Murphy
    Jun 11 at 0:57

1 Answer 1

1
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Partial answer.

Googling OEIS plus some of the numbers, I found

https://oeis.org/A057070/internal

which led me to:

31674 * 26 + 19 = 7^7

883011 * 19 + 15 = 8^8 + 8

166037352 * 21 + 18 = 9^10 + 9 (corrected)

434782608 * 23 + 16 = 10^10

31701296735 * 9 + 7 = 11^11 + 11

so we're looking for values A, B, C such that

A * B + C = 12^13 + 12 (corrected)

B = 1 to 26

C = 1 to 26

and apparently

B > C

Running this through a spreadsheet gives the following options. Not sure which of these is intended to fit some additional pattern in the previous examples.

21398641075816 * 5 + 4 (E D) (list corrected)

15284743625583 * 7 + 3 (G C)

13374150672385 * 8 + 4 (H D)

11888133931009 * 9 + 3 (I C)

10699320537908 * 10 + 4 (J D)

9726655034462 * 11 + 2 (K B)

8230246567621 * 13 + 11 (M K)

7642371812791 * 14 + 10 (N J)

7132880358605 * 15 + 9 (O I)

6687075336192 * 16 + 12 (P L)

6293717963475 * 17 + 9 (Q I)

5944066965504 * 18 + 12 (R L)

5631221335741 * 19 + 5 (S E)

5349660268954 * 20 + 4 (T D)

5094914541861 * 21 + 3 (U C)

4863327517231 * 22 + 2 (V B)

4651878494742 * 23 + 18 (W R)

4458050224128 * 24 + 12 (X L)

4279728215163 * 25 + 9 (Y I)

4115123283810 * 26 + 24 (Z X)

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22
  • $\begingroup$ Yessss! The first part is almost correct. But, there's a unique pattern, and most parts of your answer are wrong because of that. You're very, very close to the answer (the value of 12). Also, you have to change the order of some things. $\endgroup$ Jun 13 at 8:03
  • 1
    $\begingroup$ I spotted a mistake and fixed related parts. $\endgroup$
    – Ed Murphy
    Jun 17 at 0:19
  • $\begingroup$ You're actually very close to the answer. rot13(Gurer'f abguvat yvxr O > P. Naq jung lbh unir gb svaq vf nyfb jebat. Whfg ybbx ng ubj lbh qrpvcurerq gur cnggrea.) $\endgroup$ Jun 17 at 0:53
  • $\begingroup$ Well, B > C happens to be true of all six given examples. And I worked out this much simply by catching on that 8^8 [vf irel arneyl na vagrtre zhygvcyr bs] 883011, and then [fcbggvat juvpu zhygvcyr (O) naq ubj sne vg jnf bss (uvture ol P)]. If you're thinking that I worked out the opposite - why that particular choice of B - then no, I didn't. $\endgroup$
    – Ed Murphy
    Jun 18 at 2:56
  • $\begingroup$ rot13(Lrf, gung'f evtug, ohg gurer vf cebonoyl n irel fznyy reebe fbzrjurer. V pna'g znxr bhg ubj lbh znqr vg (rira znlor n glcb), ohg, jung lbh unir gb svaq, nppbeqvat gb lbh, vf jebat. Naq fbzr bgure cnegf bs lbhe nafjre ner jebat orpnhfr bs gung. Lbh tbg gur cnggrea evtug; lbh whfg unir gb nccyl vg naq trg gur nafjre.) $\endgroup$ Jun 18 at 7:46

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