1
$\begingroup$

Using only the numbers, $1$, $2$, $12$.

No concatenations allowed.

Only permitted signs are plus and division.

Brackets are not needed.

Expressions should be as concise as possible.

Typical example:

enter image description here

Fill in the right hand side for each of the three following cases:

A. $136/11$ =

B. $235/19$=

C. $4131/334$=

| improve this question | |
$\endgroup$
  • $\begingroup$ The title says "continued fractions", the question says "plus and division". The first of those is a stricter condition than the second. E.g., the trivial solutions that look like $\frac{1+1+\cdots+1}{1+1+\cdots+1}$ satisfy the second but not the first. What's the actual requirement? $\endgroup$ – Gareth McCaughan♦ Jul 5 '19 at 10:18
  • $\begingroup$ Typical continued fractions involve plus, minus, division..I will post an example. $\endgroup$ – Uvc Jul 5 '19 at 10:21
  • $\begingroup$ I know what a continued fraction is. The question is whether, as the title suggests, you literally mean that you want a continued fraction; or whether, as the question text suggests, you are content with any expression built out of +,-,/. (If the former then I don't even understand why you need to specify +-/ only. If the latter then I don't understand why continued fractions are in the title.) $\endgroup$ – Gareth McCaughan♦ Jul 5 '19 at 15:15
  • $\begingroup$ It looks as if the answer is that you did mean continued fractions, without even permitting "generalized continued fractions" where the numerator isn't 1. If so, then I don't see how there's the slightest element of puzzliness to the question. There is a standard, simple, obvious algorithm for computing continued fractions, and the only degree of freedom left to the solver is how to write each coefficient as a sum of 1s, 2s and 12s, and since each of those numbers divides the next there's also an obvious way to optimize that. Am I missing something? $\endgroup$ – Gareth McCaughan♦ Jul 5 '19 at 15:18
  • 1
    $\begingroup$ I think the concern here is that a “puzzle” solved by mechanical application of a well understood algorithm/process isn’t really a puzzle. See the comments here as well as this answer to a very relevant question on our Meta, which feels exactly like this question. Compare the guidance here. $\endgroup$ – Rubio♦ Jul 5 '19 at 23:40
2
$\begingroup$

$\frac{136}{11}$

$12 + \frac{1}{2 + \frac{1}{1 + \frac{1}{1 + 2}}}$

$\frac{235}{19}$

$12 + \frac{1}{2 + \frac{1}{1 + \frac{1}{2 + \frac{1}{2}}}}$

$\frac{4131}{334}$

$12 + \frac{1}{2 + \frac{1}{1 + \frac{1}{2 + \frac{1}{1 + \frac{1}{1 + \frac{1}{12+2+2+1}}}}}}$

| improve this answer | |
$\endgroup$
  • $\begingroup$ Yes..this is the form I am expecting for the other 2 also as shown in the example $\endgroup$ – Uvc Jul 5 '19 at 10:35
  • $\begingroup$ Check the last 2..don’t add up right $\endgroup$ – Uvc Jul 5 '19 at 10:48
  • $\begingroup$ Last 1 ok..checking 2nd one.. $\endgroup$ – Uvc Jul 5 '19 at 10:50
  • $\begingroup$ All 3 ok..got all $\endgroup$ – Uvc Jul 5 '19 at 10:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.