Solving a popular puzzle. How many boxes are there?

Can you solve this viral puzzle?

How many cubes?
Know your meme
Reddit

Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas!

If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.

If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.

Book ratings are from January 2023.

My Books (worldwide links)

My Books (US links)
Mind Your Decisions: Five Book Compilation
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews

Mind Your Puzzles: Collection Of Volumes 1 To 3
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

My Blog

Twitter

Instagram

Merch

Patreon

Press

[Qermaq]

For those confused: original upload had the title "olving a popular puzzle". It was fixed later.

[brandonvillamizar]

Don't forget to olve the puzzle by yourself, and then, watch the olution.

[ianmalcolm]

Another terrible phrasing of a question. The answer is that it’s not determinable from the information provided. How about, what is the minimum number of boxes on the flatbed?

[Hokiebird]

Lesson: Orthographic views are good for dimensions, but you need to include at least 1 isometric to give the full picture. And show your hidden lines!

[Archy_The-Wizard]

It's even possible to go as low as 21 boxes if you ignore gravity.

[stromboli]

If the boxes are filled with helium, they don't fall and you can have an empty spot under a box. This allows for several more boxes to be removed.
Alternatively, the boxes underneath can be slided to non-integer grid positions so two boxes can carry three.

[ahmadmazbouh]

my favorite hobby in my free time is olving puzzles
I love olving

[noc]

Lowest number is 1.
If you are dealing with cargo thieves, there is no reason there wouldn't be one box with lines drawn on it.

[ShawnFFHellcat]

My first thought with these puzzles is "Assuming I take it at face value, then the answer is ____, but technically there are xyz number of answers"...

[erikziak]

After looking at the picture: Since it is drawn without perspective, we do not know if there are any "voids", like the middle row of lower boxes having lower height, because it is indistinguishable from the image. If I were to assume that the whole thing is packed "fully" as the views suggest, then the number of boxes is 51.

[headcrab]

Small nitpick, but in the 35 box solution you showed, could you not remove the top and middle boxes from the top left corner of the truck? Those removals shouldn't effect the final views, i dont think.

[dbumjr]

Am I the only one who's tired of tupid worded questions that allow the olution to be any answer between 31 and 51. I can't wait to see that Simi truck driving down the road with that awesome 31 box tack job😉

[RobertMeredith-svdd]

At 6:12 you can actually remove 2 more boxes. You can remove them from the corner to get down to 33 boxes. It's still not the least but when you said "no more boxes can be removed from this configuration" I just saw that 2 more actually could. Nice video though. I love your content!

[rikschaaf]

I initially thought it was 35-51 before hearing the answer, but once you mentioned being able to go lower, I realized that some boxes could do double duty. If you remove the assumption that a box on the 2nd layer needs one below it (because they attach to each other at the corners or something), you can actually go even lower still.

[derToblin]

Disregarding gravity, the minimal number of boxes would be 25, because we can remove all base layer boxes with boxes on top of them from the 31 boxes solution. This solution can also be achieved using glue or strong magnets.

[jesss.]

I love these logic puzzles! I first said “Well they want me to say 51, but the real answer is 35” and when you said “31” I was pleasantly surprised! I had to pause the video and figure it out again!

[kokilabendamor]

Thank you for olving this popular puzzle! I was able to solve it, but i didn't know how to olve it. Thank you!

[jasilos]

7:20 you could remove the boxes from the bottom layer on which are holding the upper boxes in middle and so the upper boxes do not fall you must place underneath them some kind of support. If you do that the number of boxes goes as low as 27 boxes and 4 supports that aren’t boxes

[johnburgess]

Here's another "hypothetical" answer. The bottom layer need not be completely filled with 21 boxes. You can remove some middle boxes leaving a hollow space the size of some boxes. If some of the upper boxes are massless, they can sit above the hollow spaces and the air in the hollow areas will support boxes above them (like a piston in a cylinder). I didn't actually count the minimum number of boxes in this configuration, since it's sort of cheating. But, in so many puzzles, we assume "ideal" conditions in which there is no mass, no friction, etc. So, in the ideal situation, with some massless boxes sitting on a cushion of air, you could end up with fewer than 31 boxes.

[Silas_MN]

I got 33-51 inclusive as my answer before watching the whole video, reaching 33 by doing the 35 solution and then removing the top two boxes from the back corner. if I'd thought it through a bit more, I would've reached the same conclusion you did