# 72 + 96 = 120, is it possible?

I came across the following riddle:

How is it possible for $72+96=120$ to be correct?

• giannispapav, where did you find this riddle? Can you please provide a source? – El-Guest Aug 21 '18 at 17:23
• @El-Guest it is from a website which is not in English – 1123581321 Aug 21 '18 at 18:22
• Ah I see. As a heads-up, questions like this are generally considered too speculative (especially if you don't know the correct answer ahead of time) since they can often invite a lot of opinion-based answers which may all appear to be correct. Since there isn't a lot of detail, it is hard to tell which answer is objectively correct! Just wanted to give you a heads-up for the future in case this or any similar questions that you pose are closed. – El-Guest Aug 21 '18 at 18:27
• Even if it's a non-English website, you should link to the source. – Glorfindel Aug 29 '18 at 7:43
• grifoi.org/empneyshs-alytoi-oloi.html – 1123581321 Aug 29 '18 at 8:28

## 3 Answers

This is the

side lengths of a right-angled triangle, where the two shorter sides have length 72 and 96; and the longest side has length 120. (Note this is a 3-4-5 Pythagorean triple).

Essentially,

if you travel north 72 units and then east 96 units, it's equivalent to travelling northeast (not exactly, the heading will be $\tan^{-1}\left(\frac{4}{3}\right)$ radians) by 120 units

• but that doesn't really mean 72 + 96 = 120, does it? – Joe-You-Know Aug 21 '18 at 17:10
• It can, if you use a distance interpretation (found in my edit) – El-Guest Aug 21 '18 at 17:11
• Nice explanation, I'll give you a +1 for that. – Joe-You-Know Aug 21 '18 at 17:14

Answer :

$72^2 + 96^2 = 120^2$

• Welcome to Puzzling.SE! Thank you for your answer, it is very much correct; although if you look at my answer above you'll see that I have already given the same answer as you (although phrased differently). Please try to ensure that answers you give are different from previous answers! Also, to avoid spoiling a puzzle for other puzzlers, please use spoiler tags >! in front of your answer. Thanks very much and happy puzzling! – El-Guest Aug 21 '18 at 18:03

Let's assume

you want to bake a huge apple tart with apples from your own garden. You picked 168 apples (72 + 96) but many of them (96) have turned brown on one side or have a worm, therefore you halve those and throw away the bad halfs. What remains are 120 whole apples (if you count 2 halved apples as 1 whole).

What I want to say is:

72 + 96/2 = 120