First, here is a clip of my good self on BBC Breakfast speaking about Paranormality….

OK, enough of me.  Here is the Friday puzzle….

John lives in a house that has the reverse numbering to Jane’s house (so, for example, if John lived at number 56, Jane would be at 65).  The difference between their house numbers ends in 2.  What are their house numbers?

UPDATE: Neither John or Jane live in a house numbered between 1 and 10, nor in a house numbered over 99!

As ever, please do not post your answers, but feel free to say if you have solved it and how long it took.  Solution on Monday.


  1. This isn’t a puzzle. If you make it harder by asking people to state a general solution and prove it, then at least it has some use as a revision of how subtraction works. If you’re content with a single answer discoverable by trial and error, it isn’t even that.

    Now, as for the puzzle that I sent Richard seven months ago – which has been eagerly awaited by at least several people here – I’m not going to wait any longer to see it used as a Friday Puzzle. I plan to post the question on my blog on Monday. If I run out of time on Monday, I’ll post it on Tuesday. Regardless, I’ll let everyone know when it’s up by posting a comment on Richard’s solution thread.

    All will soon be revealed. The time of waiting is almost over. (And a week after that, I’ll post the solution, as well as some deeper analysis for the geeks.)

    1. Flakko, sheeshing at people for making a decision that just happens to be different from the decision you would have made isn’t going to win you any favours.

      I’ve picked a date for the Big Reveal, and I intend to stick to it. You might not see the merit in doing it that way, but that just means our values differ. There’s no call for insinuating that your values are obviously best.

      Final word. Will not respond to further criticism.

    2. “…the Big Reveal…” — you’re talking about your ego, right? A puzzle so amazing it’s been roundly ignored by all who have seen it in the last 7 months… I can hardly wait! 🙂

    3. Flesh-eating: I’m not sure why you say that it’s not a puzzle. If I’ve read you correctly, you are saying that it’s not a puzzle simply because it can be solved by trial and error. But that’s only _one_ way to solve it. You can also use logic, patterning… which is what I, in my admittedly hamfisted way, managed to do in about two minutes.

      Some of the Friday puzzles I can do, some I can’t. That’s one of the things, I reckon, that makes them interesting – the variety. I wouldn’t want them all to be variations on the same thing week after week. It would probably get dull very quickly.

    4. “The time of waiting is almost over”

      Blimey, this is going to be something special!

      Seven months we’ve waited! The time seems to have gone so fast.

      No, wait, no it hasn’t. I had no idea that I was waiting. At least *several* people have been waiting tho’. Several people! That’t even more than a few!

    5. More that it can be solved very quickly by trial and error, and without any forethought. There are some excellent puzzles that require trial and error to be used in interesting ways, where you have to think about how to systematically check all of the possibilities. This is not one of those.

      Couldn’t agree more with the need for variety, but I think the variety should be in the type of puzzle, not in whether or not it presents a challenge. For example, I liked last week’s, but I wouldn’t want all of them to be based on puns. (Indeed, having fewer easy ones would surely add variety.)

      Regret that I responded to Flakko. Shouldn’t have let myself be provoked. I was irritable partly because of an empty stomach – I need to go eat something.

    6. Hey, way to hijack someone elses blog. ‘sheesh’ is appropriate. You are as bad as people who post dating website ads in comments. No, you’re worse.

  2. Interesting puzzle, got a solution within 45 secs, based on this got further solutions as well in the next half a minute.

  3. Took 2 – 3 minutes, and I had to resort to pen and paper, but then I’ve always had more trouble with the arithmetical problems than the linguistic or logical ones. Good way to wake my brain up.

  4. I’m embarrassed to say that I made a spreadsheet to find the solution. I probably should have just thought a bit harder.

  5. About two minutes… which is pretty fast for me. I bet there are more answers than the one I got as well, though.

    1. some clarification … 2 solutions in 2 digit numbers … otherwise there’s an infinite number as stated below.

  6. I think there is a pattern resulting in an unlimited number of possible answers: (if the “Johns number 56 would be a solution ….. 5X6, 5XY6, 5YXZ6 and so on would also be solutions),..

  7. Great puzzle Richard!

    Got it by luck in about 3 mins. Then worked out a general solution with help from Excel.

    Think you need to state you only want a solution for 2 digit numbers otherwise there are infinite solutions.

  8. Got it immediately, strangely. I’m usually not that good at maths puzzles. Maybe I’m wrong — my solution has a two digit difference that ends in a two, is that what I’m supposed to have?

  9. I’m really the worst here, as Carl I needed a xls spreadsheet to find the number out (or better, he gave me the idea), then I only found 1 solution in two digits numbers, and still I didn’t get the patter….lazy brain!!! 😦

  10. About two minutes – half of which was trying to think of possible answers, the other half was playing in Excel to produce the solution.

    Col A: basic numbers 11-49; Col B: using value/left/right to produce the swapped version; Col C: the subtraction.

    1. There may be solutions in the hundreds (e.g. 123 and 321) or even thousands (e.g. 1234 and 4321), but I took the implied assumption that the two houses were numbered between 11 and 99 (so discounting one possible solution involving a house number below 10, as house numbers below 10 generally aren’t prefixed with 0).

      There is a clearly defined pattern throughout the range, which involves multiples of a certain number. I think it’s safe to say that any other terminal digit to the subtraction couldn’t produce a unique solution.

    2. The difference between 123 and 321 ends in 8, not in 2

      The difference between 1234 and 4321 ends in 7

      Did you or I misunderstand the question?

  11. 5 minutes for the general case. As is often the case, there are more solutions than Richard thought. In this case, there are an infinite number of solutions, i.e. 1430799 and 9970341.

  12. Got it! After 2-3 mins’ consideration, a pattern started to emerge (I think!). A bit of quick math confirmed I had the (a?) right answer.

  13. The concept behind this can be used for a good mind-reading trick. All you need is a book with around 100 pages and to memorise a handful of words…

  14. The difference between their house numbers ends in 2.

    It is not stated that the difference of the house numbers has to be positive…
    when applying the rule to negative numbers … there are still a number of solutions (even after the updated limitation to two digit house numbers)…

    I think it is fun searching for loopholes…

    (so by the way thanks for the blog… )

  15. hmmm… I got a solution in about 2 minutes but not sure it’s correct. The numbers, when subtracted, do end up with a number ending in 2 but I fear it’s not the correct one although it satisfies all the conditions. Time will tell.

  16. 1 min. i cud have wrote a program and solved it in .001 seconds, but the program itself would take 3-4 minutes to write.

  17. Saw you on Daybreak the other morning along with Colin Fry. Christine Bleakley’s body language was very striking. You could tell she absolutely despised Colin Fry, she could barely bring herself to look in his direction and stop herself shaking her head when he was talking. She has gone up in my estimation.

  18. One minute to get the solution algebraically and then 10 minues to fail to work out how some of you have two solutions (other than the trivial alternative) Still puzzling that.

    What do we think about the ethics of Excel? Isn’t the point about these things to hold a mirror up to how we think about problems? Interested in yoru thoughts.

    1. I got the solution after a few minutes of trial, then spent some 10 min on a formal algebraic solution which proves there is exactly one ordered pair (a, b) with 11 ≤ a < b ≤ 99.

      Simple puzzle, but has its joys.

  19. Took me forever! Am not very good at maths and had to write all the numbers between 11 and 99 down. I have one answer though! Can’t figure out why some of you have two answers . . .??

  20. two minutes to find the proper digits …
    … and four hours to find out later that I forgot to re-reverse the solution to match the house numbers.
    I guess the psychological trap was here.

  21. yay, got it!!!! pretty much once you “work out” the “first two” its easy to figure out (after you test the pattern a couple of times to make sure it “works”).

  22. It took me three two minutes. I started writing down equations, realized I didn’t have enough information, and then started thinking. At first it seemed to me like there would be more than one right answer, but the more I think about it the more sure I am that there’s only one.

  23. Seriously 2 answers? Please don’t tell me some of us swap the numbers around and call it another answer. :S Which you could but no need to state it as another.

  24. Got the trivial solution with a number less than 10 in about a minute (but it’s not allowed – not sure why?), took another minute to find the alternative solution.

  25. Regarding the BBC footage, I think the two presenters came across as quite hostile and ignorant in some of their questioning. Obviously they didn’t arm themselves with the facts prior to the interview.

    1. I agree. I found watching them quite uncomfortable. Richard was clear and well composed, of course, which made it a bit easier to watch.

  26. It took me forever to figure out the logic of it, but as I started to recognize the pattern, it came to me in a flash. It took me 14 minutes from reading it to figuring out the answer. I was pretty proud of myself when I did figure out, I’ll admit. I thought I’d have to completely trial-and-error it, so coming to an actual understanding was cool.

  27. I had a very odd sensation working on this one…

    Thought about trial and error, given the relatively small pool of candidates (I found the puzzle after RW had clarified it). Then I decided it would be more in the spirit of the puzzle to try and solve it algebraically. With no pen and paper handy, I tried to jiggle some x’s and y’s in my head, pondered the tiny number of candidate differences, and the answer seemed to just fall into my brain out of the jumble!

    The length of time to run a bath, or draw one if you’re posh: about four minutes.

    FWIW, and IMHO, isn’t Excel ‘just’ a more ‘aggressive’ form of trial and error?

  28. About 1-2 minutes, of which the first minute was deciding that it would be quicker to just figure out the general solution and then work back to the specific answer Richard had in mind, after wasting time on random trial & error approaches. Once I’d decided that, solving it took only a few seconds – doh!

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