Nice simple one this week. Can you cut this horseshoe into six separate pieces by making just two cuts?

There is both a 2D and 3D solution – can you find them?

As ever, please do NOT post your answers, but feel free to say if you solved it and how long it took. Solution on Monday!

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yep

Hmm. Depends how you define “two cuts”.

took me about a minute to come up with two possible answers, both of which work, but both of which might be wrong…*lol*

Good one. Thought I got it right in a few seconds, but then it took ~four minutes to find a correct method.

This is one of the few I got faster than most people. Got it in about four seconds, where I’m usually 3X slower than everyone else. I also tested it in ginp, which told me my solution equaled 6 equal parts.

Aw come on Richard this is too easy.

Solving it in 3D was easy, then I read the question again and realized you meant 2D. Took a few more seconds, but not too bad.

Got it. Took me about five minutes, because I’d previously disregarded a solution as incorrect, and it took me another look before I realised it actually did have six pieces. Not sure if it’s what you’d call the “correct” solution, but it’s the only one I can think of.

It depends on how strict your cutting rules are.

Yep – I’ve seen this before, though….

Easy in 3D, to be honest, I can’t work it out in 2D though, not sure the question specifies that though like a previous poster says.

I worked out a 2D one (in which the pieces aren’t equal) pretty quickly but haven’t yet figured out a 3D one, or an equal 2D one.

3 seconds it’s a classic

I stand corrected if it is 2D. Not easy at all, assuming it can be done at all.

Sorry I take that back. Very easy, once you get rid of a wrong assumption.

Got it in 2 Minutes (my new high score). Remembers me to the old scool Puzzles. But i had to draw it, was unable to solve it just on the screen.

I also dont know what “2 cuts” exactly mean, have an idea, but cannot post it here until monday ! As ever, Richard didnt describe it exactly enough.

My Solution also works in 2D, so you can try with paper and scissoir. I think Richard will not post Puzzles in 3D…

Got this one quickly (couple seconds), unusual for me here.

yep – this was an easy one.

First 2 ideas were working … so 10s overall – proofing took another couple of minutes. Very easy one.

Got a flash of an idea immediately, but took 30 seconds to work out the exact details.

Well, I managed to cut in into 5 pieces with one cut (3D).

And with 2 cuts – 8 pieces.

Or even 9 !

I managed 10 pieces in 3d.

From what I am seeing, 11 might be possible, but i wont spend more time to it.

wat works for 2D.. alos provides a 3D solution..

The question seems to be if it is allowed to rearrange the pieces between the cuts?

Stopped thinking after the 9 piece solution without rearranging…

under a minute (including a few sketches)

if you fold the paper before cutting… provides ridiculous number of parts..

(P.S. the 9 piece solution was for 3D.. )

It’s a horseshoe -you can’t fold horseshoes.

@ Bernhard That’s a spoiler. What for things like that until Monday… even if you are proven wrong

I can do: 3D – up to 7 pieces (definition of cut (*)), 6 pieces “everytime”.

2D – easy with (*) definition of cut, otherwise IMHO impossible

My definition of cut:

A single straight line through the entire object from any view.

I assume you mean two straight cuts? Yes i did it at second attempt (first attempt looked OK until I counted and got…dur…5 bits), needed to just look at it a minute and as usual get rid of my assumptions – what you did and did not ask for

It’s funny, as you said you did it once you got rid of your assumptions… and yet your first two words are “I assume”.

So, no, I don’t think you can assume that…

Oh drat I knew I had assumed something I shouldn’t have – but 3D? no, my solution is in 2D and DOES use straight cuts

Martin: yes, it is easy in 3D.

Blimey, I got one! I regard myself as _considerably_ less able than you lot in that I always find these difficult (well, I say ‘always’ – I’ve only been on the list three or four weeks). But this one was breaking me in gently. 🙂 It only took me five hours. (Joke.)

2D straight away, 3D after a few mins visualising it (not enough coffee today).

I assume the pieces dont have to be of equal size?

I tried, it didn’t go well.

Anyone in here knows how to remove angle grinder marks from a cedar coffee table? Preferably within the next two hours, before the wife comes home from work.

drawing the U shape on paper took longer than solving the puzzle

If the cuts don’t have to be straight, then it’s easy to cut it into an arbitrary number of pieces, so I guess it is missing the constraint that they have to be straight?

Then in 3D was easy, I found one solution in 2D, but I’m not sure it’s the ‘right’ answer – two of the pieces are very small. In fact with this method I can make 7 pieces.

My thougth also … with non-straight cut, you can achieve any desired number of pieces…

3D immediate and 9 pieces claimed above doesn’t seem unreasonable. 2D took 5 minutes as is often the case thinking against the natural (psychological) inclination towards symmetry.

Assuming the pieces don’t need to be equal, I got this within seconds of pasting into Paint. Wonder if I’m missing a catch.

I had to paste it into ms paint!

but once i’d worked it out and checked it about a minute, 2&3D

this was fun because i could actually answer this one :p

2D: 7 pieces. (there are perforations in the horseshoes)

Got the 3d straight away still working on 2d.

Depending on definition of ‘cut’ I have a solution that generates an awful lot of pieces otherwise about 3 minutes (I’d included the word equal in my first few solution attempts)

No problem for both… 1 minute

2d – done before the picture had loaded.

3d – my 2d solution works on a 3d model, so I can’t see the need for a separate solution.

I wouldn’t define a cut as straight, but usually in puzzles like this you would have the constraints of:

– The line cannot cross over itself (you could just keep looping and make loads of pieces)

– If it leaves the body of the object then that is the end of a cut. For example a straight line across the lower half of the horse-shoe, creating three pieces by cutting off two prongs would be TWO cuts.

I’m not sure if this puzzle follows those rules though, particularly the second.

Has anyone found a solution that obeys all the above rules?

To follow to that, I have a solution which obeys the first rules and skirts closely with the second.

I follow that set if rules, although they are not quite clear.

I use two straight line cuts, both of which could be made with, say, an angle-grinder, without any break in sparks, as it were. I do not rearrange the pieces in between cuts either, although I cannot see why that should be disallowed if people want to.

Took me to solve the 2D one in 30 seconds.

Got the 2D solution fairly quickly, am saving working on the 3D solution for my coffee break!

Got the 2D solution in about 3 mins. I’ll have to think a little more about the 3D solution.

Yes. Easy for me today … seconds.

yeah. about 1-2 minutes

Done it in 3d and 2d but didn’t use the definitions of ‘cut’ given above,

2 straight lines = 6 unequal but separate pieces… about a minute

Got it in about 4 minutes

Solved it seconds…exactly how many I have no idea because I am not SIX!!! What is it with the “yeah I got it on less than a minute” comments? What is the average of the readers of this blog??

About 1 minute to finish the two.

I like visual puzzles, though I always suck at the “remove two matches to make…” variety.

done it within a minute. 2 straight cuts, 6 pieces.

So nice indeed, took me 15-20 minutes to solve it, quite fair enough lol, but also we might like to consider, keep in, or put in consideration that some discoveries or conclusions might take decades specially if it was based on a theoretical perspective, been observed via matter of facts which is a must, since that is the only difference between the Holy Theory of creation and human theories, whatever & whenever a human start a theory it is a certain to be founded as a pre-existence case somewhere else, whether at the same planet or in another planet indeed trust in that that was one of “GOD”s challenges, which when thinking about the first fact the theory will be based on is factor time, then after the subjects and etc. So now all what “i” have been telling will be conflicting with what “i” did start with, which was ” so nice indeed, took me 15-20 minutes to solve it, and almost 35 minutes to comment about it loooooooool

Thank you for your patient.

If Richard means straight cuts, he needs to say so. Nowhere does he say it currently.

I figured it out after looking at the question carefully.

With the help of playdough(!) I figured out the 3D solution in about 30 seconds (needed the playdough to test if I was right!)

Done. Instantaneously 🙂

Instantaneously too 😉

It took me far too long. But I’ve done it in 2d.

I could do a 2D solution in seconds – but had problems with a 3D solution as the shape in 3D is ill defined – it is a 2D cartoon of a 3D object and that made it tricky as I wasn’t sure of the exact shape and actually the cuts would give six or possibly more in “reality”

3D instantly. 2D about a minute, followed by another minute of wondering if I was wrong. The 2D was surprisingly hard for me to get my head around and I am not really sure why.

Thanks Richard! Love this kind of puzzle!

6 pieces with 2 straight cuts:

in 3D after seconds

in 2D after some minutes

In 3D there are this bumps on both ends. Therefore I found a solution for 11 pieces with 2 straight cuts after 20-30 min

Got the 2D version straight away, assuming straight line cuts, and ‘proving’ it in a drawing program. I got the 3D version fairly soon after too, and as soon as I saw the comment on the possibility of cutting it into eleven pieces, that sort of fell into place too…

It is 2PM and if we consider bumps at the ends of the horseshoe, there are even more than 11 pieces possible…

Seriously, I should go to sleep now

3D solution took me less than 30 sec.

It took me a while to get the 2D solution.

After I got the 2D solution it didn’t take me long to figure out how to section the shape into 9 and 11 pieces in 3D.

Got a 2D and a 3D and checked it both work if my definition of 2 cuts are acceptable in about 3 min total.

Got 3D quickly. 2 minutes for work out 2D.

about 10 seconds for a 2D solution

What is the answer please= palmerboxing@yahoo.com.au

What is the answer please, to the horshoe riddle or mystery ?

Neil= palmerboxing@yahoo.com.au

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The answer will be provided on Monday.

Almost immediately!

Playing slice-it all the time on iPad, it took me about a few seconds for both solutions.

Gardner studied the problem od slicing a dougnhut into 13 pieces with three cuts (three planes in 3D). Quite equivalent to the solution of this post, but in 3D.

M. Gardner, More Mathematical Puzzles and Diversions, penguin books, 1961, p 118

Another poorly written puzzle, when I commented on a previous puzzle they changed the wording on the puzzle and left my comment, this time it appears they just deleted the comment.

The puzzle is worded incompletely, as the answer (revealed on Monday which can now be seen as I write later) shows. The rules have to include that the two cuts are straight line ie with scissors and not with a scalpel or whatever which can cut in curvy squiggles.

Naughty naughty – puzzles must be worded properly..