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Can you find two numbers composed only of ones which give the same result by addition and multiplication? Of course 1 and 11 are very near, but they will not quite do, because added they make 12, and multiplied they make only 11.

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!

Source: “536 PUZZLES & CURIOUS PROBLEMS” by Henry Dudeney.

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    $\begingroup$ Looking at the accepted answer, I think "can't use digits other than 1's" in the title is a more fair description than "composed of only ones". $\endgroup$
    – xnor
    Nov 6 at 1:46
  • $\begingroup$ @xnor I totally agree with you. However when I post a puzzle that someone else created, I try as much as possible to use their original wording. Thanks for your comment. Have a nice day! $\endgroup$
    – Will Octagon Gibson
    Nov 6 at 5:30
  • $\begingroup$ 200 reputaion or more... $\endgroup$
    – Stevo
    Nov 6 at 10:46
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    $\begingroup$ Agree with the implication of Stevo's comments here. You encouraged for users with more than 200 reputation to refrain from answering, yet you quickly accepted an answer from a >200 rep user within 14 hours of posting (less than the standard guideline of having at least 24 hours before accepting an answer). 😅 $\endgroup$
    – justhalf
    Nov 6 at 11:09
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    $\begingroup$ @justhalf I wasn’t aware of the 24 hour guideline. Thanks for letting me know about it. Is there somewhere that I can read about PSE guidelines? I want to act responsibly here. $\endgroup$
    – Will Octagon Gibson
    Nov 6 at 11:59

1 Answer 1

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We can rearrange $ab = a + b$ to get $a = \frac{b}{b - 1}$. Then we just plug values in for b. 1 clearly doesn't work, but 11 strikes gold:

11 * 1.1 = 11 + 1.1 = 12.1

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