# How can four be the half of five? [closed]

I came across this enigmatic one-liner:

How can four be half of five?

Can you figure it out?

• 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? Mar 22, 2022 at 8:39
• Why am I getting close votes? Mar 23, 2022 at 10:46
• 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. Mar 23, 2022 at 11:12
• Oh, I get it. Thanks for explaining! Mar 23, 2022 at 11:13
• I think it would be more clear without the word "the". Mar 24, 2022 at 1:29

One answer that springs to mind

IV (Roman numeral for 4) is half of FIVE

• @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.
– DrD
Mar 21, 2022 at 14:02
• Thank you, did not think of that! but I can't edit my earlier answer, dunno why... Mar 22, 2022 at 9:31
• @HexagonalImpossibilities then four's half of four! Mar 22, 2022 at 10:32
• @user253751 indeed Mar 22, 2022 at 11:10
• @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. 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.

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!

• I'm certain that one of those upvotes is my taxman. 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 :-)

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