# It’s the Friday Puzzle!

79

An easy one this week…..What caused the recent riots in Britain?  Just kidding….here it is……

Which is a better fit (i.e., results in less wasted space), a square peg in a round hole or a round peg in a square hole?

As ever, please do NOT post your answers, but do say if you think you have solved the puzzle and how long it took.  Solution on Monday.

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

## 79 comments on “It’s the Friday Puzzle!”

1. soonerdvm says:

2. James says:

The question’s pretty ambiguous, so I’ve worked out how much space the smaller shape takes up as a percentage of the larger shape. I won’t say how, but hopefully that’s good enough as an answer.

3. Is the picture a clue?

4. Tom Pedersen says:

I got an answer in about 5 minutes, but I’m not sure if it’s correct. Makes mathematical sense, though 🙂

5. steve lazarus says:

About a min before it dawned on me.

6. Alex says:

Think I’ve got it, now to wait till Monday to see if I’m right!

7. lehcyfer says:

It’s ambiguous all right – took me about 5 minutes to calculate and compare ratios of area left to area of hole.

I’d add to the question phrase: “when the round hole and square hole have identical area”

• Mike Hitchcock says:

I don’t think size matters (this time!) it’s the ratios that count.

• lehcyfer says:

When sizes of holes are equal, there is no need to calculate the ratios, but I agree – the wording is “which is a better fit (i.e., results in less wasted space)” so the size is irrelevant, only ratios matter.

8. Jenny says:

Took a couple of mins drawing pictures to find an elegant solution.

9. Jenny says:

PS I can’t see your picture (am using Chrome)

• M says:

Me neither. Click on it,

• Dave S says:

“Doctor, it hurts when I do this”

“Then stop doing that”

10. M says:

First puzzle: 10 seconds.

Second puzzle: two minutes or so.

11. Jimbo says:

3 minutes and a side of A6. Now for the 2nd question…

12. nanda says:

First is a really puzzle to me still didn`t figure it out.

(How to control 300-500 idiots is a puzzle). However, sri lanka forces eliminated 10,000 idiots to bring peace.

The second: 3 min

13. marie says:

Straightforward math. 17 minutes – but it is late!

14. Did it the long way with pen & paper, about 5 min, arrived at an answer based on constant peg area. Sure I’ve missed something easy though.

15. neil j says:

Interesting, never thought about this before. Am going to try other shapes ratios for no apparant reason.

16. Sian says:

10 mins, mostly due to a schoolgirl error of mixing up my 2piR and my piR^2 ‘s!! D’oh! Suspect that’s possibly how the riots started too…! 😉

Solved problem for “wastage as a percentage of the hole area” as agree puzzle wording a bit ambiguous.

17. marie says:

I didnt use constant peg area. I kept constant the circle diameter. Going back to do the ratio which should be independent of sizes

First puzzle is just too easy.

Seconds puzzle:

Just visualizing it, I’ve got an answer – 30 seconds or so

I *think* it’s right, but now to prove I’m right….

It took too long to prove, as I had a brain freeze.

Once past that – sorted, and proven.

19. marie says:

Well that went quicker and more satisfying – about 3 minutes with pencil

20. marie says:

test

21. Greg Bailey says:

That’s quite a neat answer (assuming my reasoning is correct).

22. Nerd says:

3mins of scribbling, thanks for warming up my maths brain for the day.

23. Goliath says:

Fiddling around in Excel for 12mins…

As for the first problem – not learning how to solve one of Richard Wiseman’s problems – ups, I gave it away now, apologies.

24. TS says:

It’s not rioters or looters in Britain.

It’s the beginning of a zombie invasion.

You know what to do. Shop smart, shop S-Mart.
Everybody got that?!!!

25. Berhard says:

it depends on the target to be achieved, —- with or without deformation and if the peg is for taking torque or shear loads…
it may be possible that the definitons of holes may influence the result… are the holes of the same diameter or of the same area?

When using a normalized approach, i.e. the area expressed as a fraction of the area of the hole, the … wins…
In case the holes have the same diameter / width the … wins, too…

26. Berber Anna says:

As for the first part, my guess (at least for the looting part) is a disconnect between money and effort, making money not something that one earns, but a privilege that is either given or not given (making it feel unfair that others may have more of it). Well, that and just plain old monkey see, monkey do. Probably more of the latter. Teens are sensitive to peer pressure, after all.

As for the second, there’s one answer that intuitively feels right. So it’s probably the other one. 😛

• Jimbo says:

True. When CEOs, bankers, royals, sportsmen and celebs appear to get lots of money for very little effort it becomes hard for the rest of us to accept getting little money for lots of effort.

27. Berhard says:

forgot to “answer” the first Question:

First, what caused the recent riots in Britain?

Presumably, a Butterfly flapped it’s wings in Brazil….

28. Dave S says:

Just when you thought there was one place left safe from political prattle 😦

As for the actual puzzle, there’s no way to answer it without further information. Constant area? Constant width/diameter?

• Anonymous says:

It is solvable, you use example dimensions, then calculate ratios. The ratios will be identical no matter what dimensions you use to calculate the areas.

29. JKG (@jkg) says:

A few minutes of doodling and fiddling with equalities gave me an answer I’m happy with on the square/circle thing.

I don’t think the riot question will ever truly be answered….

30. Juan AR says:

Intuitively about 30 seconds. Calculating about 4 minutes. With the two methods I arrive to the same result. 🙂

Round peg

• Berber Anna says:

Square peg

32. 1-2 minutes to calculate. Now I’m going to eat a pie.

33. A. says:

Drew some pretty pictures, then some even more pretty equations and got an answer in about 4 minutes.

34. Confmat says:

Second question, about five minutes. And I think the answer is always the same no matter how you interpret it.

The first one is a trick question, it should be:
“How do you stop them happening again?”

35. Mark says:

The only honest answer to the first question is I don’t know, though I do look forward to the answer on Monday. Second question was easy enough, just took a while trying to remember my high school maths. Probably about 10 mins.

36. Jerry says:

A minute or two to do the calculations.

37. Kristian says:

Had an initial hunch, which was then confirmed by my math. About 5 minutes all in all.

After reading the comments I see how the question can be ambigous (but apparently it didn’t catch my eye at first).

38. Jerry says:

On problem two, that is. Problem one has multiple answers. I am still working on that one.

39. Phil McCavity says:

Round peg

• Goliath says:

Where in the question above does it say to give the answer away?

40. Nochsta says:

The answer depends entirely on the size of the peg compared with the size of the hole.Presumably, either the round peg and round hole are different sizes, or the square peg and square hole are.

• Drew says:

What about using a square peg and a round peg both with the same area?

• Jimbo says:

I think you have to assume that the pegs fit the holes as well as they can be expected to. I other words, they touch the sides.

41. Drew says:

A few minutes of pen and paper maths, and very much enjoyed it, thanks!

42. Todio says:

I assumed that the holes would have a constant area (I assumed 1 inch square for the square one and thus one square inch for the round one) That helped the solution immensely. 5 minutes.

As for the first question: it’s similar to a chemical reaction that requires a catalyst. Put two chemicals together and nothing, add a catalyst and ‘boom’, reaction. Put unemployed youth under economic and social stress, add booze and you just get more stress and frustration but add the catalyst of an allegedly unnecessary killing of a youth by forces of the government (translation: oppression) as the catalyst and ‘boom’. (the same can be said for the catalyst of lots of youth jammed together. Add a football match and…)

43. No, the question is not ambiguous at all. It’s clearly worded. Size of the hole or peg doesn’t matter as it’s a ration thing. I.e how much of the hole in each case is filled up with a peg that just touches the sides.
Took about twenty minutes with my eyes closed in the hot tub after breakfast.
Worked out the square peg in a round hole a couple of different ways to exclude brain error.

• James says:

The question doesn’t actually mention ratios or proportions, which is why I called it ambiguous. It talks about “less wasted space”, which could mean less as a proportion of the volume of the peg or hole, or could equally just mean less space in absolute terms. If it was the latter, then clearly a very large square peg in a very large round hole would waste more space than a very small round peg in a very small square hole, and vice versa. But I assumed that he meant ratios too, in which case it’s pretty straightforward geometry.

44. A couple of mins with a pen and paper (oh, and a calculator to check.)

Square peg.

• Jimbo says:

You’ll need a bit longer then.

45. Henry Ruddle says:

Clearly, the riots in London were either caused by President Obama or the Tea Party. Those are the only two choices offered by America’s pundit class, and our job is to simply believe.

Speaking of idiots making things more difficult than they need to be, the answer to the second question is “It depends on how hard you swing the hammer.”

46. SeleneBlueSky7 says:

I do think I know this. Not really a question tho.

47. marie says:

Intuitive answer to the first: “shock doctrine” reaches Britain. Britiain refuses to lie down

48. debbieinmallorca says:

Couple of minutes – Wow I love maths!

49. About 90 seconds, leaving answer in a ratio of pi. Interestingly. the area not filled by the round peg in the square hole is the same ratio as the area between 4 tins packed in a square lattice arrangement. Yup. Maths is cool. And important.

• Jimbo says:

But the answer is not a number, it’s a shape (or two).

50. Nige says:

About a minute. Hope I’m right for once!

51. Michael Sternberg says:

A few seconds to put the math together, and a minute or two to figure out the details. The problem is incompletely stated, so the solution is parametric.

52. Keith says:

Why are manhole covers round?

• Different question. Still a good one, but the reasoning is not the same.

• TS says:

Easy. If it is round, the cover can’t fall into the personhole.

53. fri says:

If you assume that the radius of the circle is the same in both situations, you can calculate it. If the radius is not the same, you can find a solution where the wasted space is identical in both situations

54. moo says:

The question is phrased vaguely and the image in the question misleads as to what the question might be getting at. It appears that what is actually being asked is “Which gives the smaller ratio of unoccupied space – drawing a circle inside a square so that it touches on all four sides, or drawing a square inside a circle so it touches on all four corners?”

55. Ross says:

Had to look up the laws of 45 45 90 triangles, but I got the answer in about 5 minutes.

56. Jon d says:

Hmm pretty sure I’ve seen equilateral triangle person hole covers which don’t fall down their own hole either… Which doesn’t get us anywhere with the peg problem but at least rioters wouldn’t be able to roll them at the police.

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57. Anonymous says:

Rounding, one has 21.460% waste, while the other has 36.338% waste. (I’m not saying which is which, though.)

58. duckfish says:

got it, 10 second to understand the question, less than 1 minute to caculate

59. John Rowland says:

Got this in a few seconds. Then I should do – It’s on my website…

60. Pennie says:

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