I came across this enigmatic one-liner:

How can four be half of five?

Can you figure it out?

  • 7
    $\begingroup$ Having seen the answer, I think the following phrasing would make make for a better, less ambiguous puzzle: How can 5 be half of 4, and 4 be half of five? $\endgroup$ Mar 22, 2022 at 8:39
  • $\begingroup$ Why am I getting close votes? $\endgroup$ Mar 23, 2022 at 10:46
  • $\begingroup$ The close votes so far all give the reason that the question invites speculative answers ( see this meta post ). I'm afraid my previous comment may have triggered that. Personally, I disagree. When the tags are taken into account none of the alternative answers can be correct. My phrasing would nail it down a bit more without the need for tags, but that does not mean that the question is not specific enough as is. $\endgroup$ Mar 23, 2022 at 11:12
  • $\begingroup$ Oh, I get it. Thanks for explaining! $\endgroup$ Mar 23, 2022 at 11:13
  • $\begingroup$ I think it would be more clear without the word "the". $\endgroup$ Mar 24, 2022 at 1:29

7 Answers 7


One answer that springs to mind

IV (Roman numeral for 4) is half of FIVE

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    $\begingroup$ @HexagonalImpossibilities. A suggestion. As a courtesy to puzzle solvers, who prefer to solve it without looking at a direct answer, please use rot13 to hide your comment. Seems like it gives the answer out. $\endgroup$
    – DrD
    Mar 21, 2022 at 14:02
  • $\begingroup$ Thank you, did not think of that! but I can't edit my earlier answer, dunno why... $\endgroup$ Mar 22, 2022 at 9:31
  • $\begingroup$ @HexagonalImpossibilities then four's half of four! $\endgroup$ Mar 22, 2022 at 10:32
  • $\begingroup$ @user253751 indeed $\endgroup$ Mar 22, 2022 at 11:10
  • $\begingroup$ @infinitezero thanks for your suggestion, though I personally prefer this tool. Anyway, @ hexomino, my reasoning was "rot13Pbaireg 4 gb ebzna. VI ner 2 yrggref, juvyr svir ner 4 yrggref. Sbhe vf gur unys bs svir!". But yours is close enough and also logical, so yeah. $\endgroup$ Mar 22, 2022 at 11:16

If you make a pentagon,

/ \  

and you cut it in half from top to bottom you get:

 /|  |\  
|_|  |_| 

that is, you get two shapes with four corners each.


Another (kind of linguistic) answer:

Since the word half, at least historically, means "one of two approximately equal parts" (for example, Merriam-Webster gives the following example: “Which half do you want?” “I'll take the smaller half.”), we can say the following: Four is the half of five, as long as one is the other half of it!

  • 5
    $\begingroup$ I'm certain that one of those upvotes is my taxman. $\endgroup$
    – dotancohen
    Mar 22, 2022 at 10:06

Four is the half of five if five is two times four. Considering the multiplicative group of integers modulo $3$, we have:

$$ 2 * 4 \equiv_3 8 \equiv_3 5 $$

So five is two times four. And so four is half of five.


There are literally an infinite number of solutions of the form:

In the list {25, 25, 25, 25, 100}, four is the half of five :-)

  • 2
    $\begingroup$ @infinitezero rot13(Sbhe vgrzf (sbhe gjragl svirf) ner unys bs svir vgrzf (sbhe gjragl svirf naq bar uhaqerq), nf gurfr gbtrgure znxr gjb uhaqerq.) $\endgroup$ Mar 22, 2022 at 9:33
  • 2
    $\begingroup$ Well, four are the half of five. $\endgroup$
    – Kaz
    Mar 22, 2022 at 18:18

If you draw 5 in Roman Numerals and then draw a line cutting it in half, you get the Arabic numeral 4 (upside down) perhaps?

\  |
 \ |

\ /|
 X |
/ \|


Take 4 in binary: 100
Take away zero, twice (4-0-0 = 4): 1

Take 5 in binary: 101
Take away zero, once (5-0 = 5): 11

Obvious mathematics is obvious. Why are you troubling me with this?


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