As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

I am thinking of four numbers.  The mode is 1, the median is 2 and the mean is 3.  What are the numbers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.


  1. Isn’t this a typical primary school maths question? 5 seconds to estimate an answer, a further 10 to check that it was right.

    1. It really amuses me that you say this is a primary school maths question, then ‘estimate’ an answer and check it’s right! Thanks for brightening my morning up 🙂

  2. For you that foresake… if this didn’t make you shake the rust out of the old, grey cranial folds for a minute, you are either hopelessly unsexable, or 14, or both.

  3. Barely into my first coffee of the day, and I couldn’t remember how to do the median. After looking that up, it was just writing the numbers down.

  4. Medians and modes are not really concepts that usually make much sense with very small sets of data. Strictly speaking, the median is not well-defined when there is a small set with an even number of members. I assume everyone above is applying the traditional kludge, but one should be aware it isn’t strictly correct.

  5. You don’t need to guess any numbers- you can work it out! Trial and error is probably never the solution to a puzzle on here! Very easy this one

  6. 30 years on from the last time I had anything to do with modes or medians, was pleased that it took very little time. Just a bit hesitant about the median of four numbers to begin with, but common sense & logic prevailed.

    1. Actually – I take that back. With four numbers there is no “the” median, although there is a standard practice. My answer assumed this standard practice for a median when there are an even number of numbers. I also assumed that the numbers are all integers.

    1. Well I’m still working on it ………..

      I’m not as clever (or self satisfyingly smug) like what the others are here. IMHO what’s the bl**dy point of posting how many nano-seconds it took you? Do we take it that they record similar times in the bedroom department.

    2. To Dave’s Neighbor (not the one next door but in the apartment opposite the hallway),
      I think they spend far more time on their puzzles than in the bedroom department, so they don’t record such long times there.

  7. About 10 minutes until my final answer. Wasn’t happy with first answer. eventually Had to look up the rules for medians of even sets of data.

  8. And there could be an infinite number of solutions, depending on how you kludge the definition of “the” mode. (And verifying that is the only thing that pushed my solutin time past 10 seconds.) These terms really don’t apply well to small sets.

  9. I was truly ashamed to admit that I had to look up all three of those terms 😦
    But once I refreshed my memories it was a nice and easy one.
    For a brief moment, I was tempted to state that you picked truly elite numbers 😉
    Then I realized that I was slightly off with that guess.

  10. I know what median and mean is, but I am not familiar with mode in maths – is the wikipedia definition correct? (the most common element in the set)?

  11. I knew two members of the set immediately (as they satisfied one condition), it took a couple of seconds to get the third value (so as to ensure another condition was met with a whole number), then a few more seconds to get the final value (to ensure the remaining condition was met).

    If Richard really wanted to challenge us, he should have given us a larger set and values for the geometric and harmonic means 😀 (Actually, is there a set of numbers that would give differing whole number values for all five averages?)

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