# It’s the Friday Puzzle!

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First, we have just released some new research showing that millions of people in the UK are now sleep deprived.  If you want to discover if you need more sleep, we have created The Sleep Test.  Hope you find it interesting.

Second, here is the puzzle. Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

My friend has 4 pieces of jewelry – a ring, a necklace, a bracelet and a brooch.  Given that she can wear any number of the objects when she goes out, how many combinations of her jewelry does she have to choose from?

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.

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

1. Barry Goddard says:

I hope to post the answer below a little later. So don’t read on if you’re one of those boring people who expects everyone to obey Richard’s instruction.

• Vinay Jha says:

Meanwhile you solve. Once you get the answer do post it.

• Julian says:

Good news! Richard already does this for you, so you don’t even have to be that boring.

(Oh, and about 3 seconds, plus another 25 seconds looking for a catch that I might have missed.)

• Barry Goddard says:

Including wearing none of the item, did any one get 18?

• Garry Boddard says:

Haha. Wrong again, Bazza.

• Stu says:

“I hope to post the answer below a little later. So don’t read on if you’re one of those boring people who expects everyone to obey Richard’s instruction.”
.
“I have so little going for me in my life that the high point in my week is showing off that I can solve a problem to a group of strangers on the internet. And I have so little regard for those strangers that I don’t care if I spoil things for them”.
.
And, best yet, you then got the answer hopelessly wrong. So not just a dick, but a thick dick as well. Congratulations!

• Barry Goddard says:

The answer is 25, including wearing none of the items (4*3*2*1)+1

• Stu says:

Still being a dick. Would you care to explain WHY you are choosing to be a dick about it? Or do you feel that would compromise your persona as a uncaring rebel who flouts the rules of convention by (whisper it) posting solutions to online quizzes where you’ve been asked not to? (several people swoon).
.
Has Richard upset you in some way, that you have decided to repeatedly ignore his request not to post answers? Or is it some more deep-seated thing, like you never got called on in school? Seriously, why the need to try to spoil things for others?

• Tony says:

I think you’re right first time, Stu. He’s a dick who craves attention from strangers. And we’re giving it to him, sadly

• Tony says:

Apparently he’s not only a dick, he’s a deluded Astrology nut as well!

• Richard's Dorkings says:

Barry may be an “astrology nut” Tony, but at least he is not one of those fundamentalist atheist fanatics.

2. Vinay Jha says:

Got the answer while reading the Q. It is question of whether to wear it or not

3. Chris says:

4. Vaibhav Garg says:

Can she choose to not wear any jewellery?

5. Roy Gillett says:

Took about 10 seconds to spot the pattern. Another 10 wondering whether no jewellery counts as an option

6. VicinCA says:

Easy enough (3 sec) but then the lurking question of whether none is an option.

7. Anna Lyse says:

638 combinations… since the necklace is made out of individual chain segments which can be worn individually. Who’d have thought of that, he?

• Per says:

That would be tear not wear 😉

8. Slange Navarr says:

About a minute. I know there’s a proper maths way to do it but I can’t remember what it is, so I just listed the options on a bit of paper.

9. Cowardly Troll says:

One minute

• Barry Goddard says:

It’s the four summations of nCr for n=4 and r=1 to 4

• MathMiles says:

Why have you omitted r=0 as a possibility?

10. Noticer says:

3 minutes

11. Now this one I actually remembered from probability math classes. I too found an answer within seconds and then spent some time looking for a catch.

12. Eddie says:

Interesting this one because it’s not a typical permutation or combination.

13. mgm75 says:

Took me about a minute using Excel. I am shocked no muppet (or troll) has posted the answer yet, and the post has been up a whole hour

14. Barry Goddard says:

Quite easy, it is simply 4*3*2*1 which is 24

• Barry Goddard says:

Actually using nCr it’s 4C1 + 4C2 + 4C3 + 4C4 = 15

• Uh Uh – “Given that she can wear any number of the objects” , you are missing something

• kroketje says:

I got 15 as wel, like Barry!

• Anonymous says:

Interesting that 15 also obtained for no. of four digits in binary (=2^4 -1). Also see Alex below for the 5 digit case, total 2^5-1 = 63. So nCr (r=1 to n) = 2^n-1. Must prove that some day.

Meanwhile…. Come on Cambridge!!!! (Boat race)

15. Hugh Janus says:

Why the American spelling? It should be “Jewellery”

16. Barry Goddard says:

One again many people have used my name to post here. This is not productive of either Richard’s time or mine or theirs or yours.

I will answer in the Spirit that Richard requests. Using my skills on producing star charts it was immediately obvious that this is a Yes/No question – in fact four Yes-no questions forming a simple Truth Table of possibilities.

Thus it took me only a fraction of a second using my intellect.

Had I written the truth table down (this is a valid tactic in solving this puzzle) I do not know how long it would have taken. That would depend on the pen I use.

Those who would me me can now go back to sleep.

17. Stan says:

Ahhh, what a pleasure to have something that takes a little thought but is easily done. Took me about 7 seconds. Barry Goddard’s approach of using random formulas was cute. I suspect many humans go through life that way with confidence.

18. Eddie says:

Does she wear anything else apart from the jewellery?

19. Lazy T says:

She has just one option since those two lying kids nicked the lot.

20. CJ says:

Each of the n items can be worn or not worn (2 choices). So the solution can be understood as 2^n

21. Barry Goddard says:

Well, despite all the idiots above whose little minds are amused by stealing my identity, I will help to explain the problem for those who are still struggling.
The correct answer is 132. See if you can work out why. The clue is that some of the jewellery can be worn in different ways.

• Tony says:

Can you save us all a bit of hassle, Barry, and just stuff it all up your arse?

• Miss Chili says:

Ah, yes: she could wear the earrings in her nipples or her belly button, for instance.

Okay, perhaps not, but different times require different jewellery.

• Miss Chili says:

Re: Tony’s suggestion below
All of it at once or in different combinations? :-S

• Eddie says:

Not many people pushing your button today Miss Chili.

22. snoma says:

I’m thinking either Richard should ban Barry from commenting or just disable the comments for these friday puzzles.

23. MathMiles says:

I wouldn’t get too annoyed with Barry Goddard. It’s been obvious for a few weeks now that several people are posting with that name and some are using it just to have some fun posting nonsense.

• Calgacus says:

There’s been a bit of cyber bullying going against our Barry. Some people need to take a look at themselves in the mirror.

24. Barry Goddard says:

I do wish that people would refrain from identity theft. It is extremely unbecoming and most uncooth. I do not wish to keep to Mr Wiseman’s rules as he is not a believer in the power of astronomy as I am. It really is a poor show to see the many responses that took longer than 1 minute to solve this. The answer is in the stars my friends! There is a clue regarding the American spelling of jewelry and its reference to the combinations available. Many American astrolomers entwine a moonstone ring in a necklace chain to act as something similar to a pendant. It becomes one piece of “jewelry”…!

• Garry Bollard says:

I fully concur

• Hugh Janus says:

I tried to ring my wife in Banglelore for a clue but she refused to broach the subject. What a choker

25. John Cartwright says:

About 0.2 seconds to calculate the answer, about 20 seconds wondering why this week’s puzzle is so obvious and easy, about 10 seconds wondering if there is some sort of twist that I’ve missed, and about 2 minutes wondering why so many of the “spoiler” answers given in the thread already are wrong.

26. M says:

I worked out how to solve it within a minute, and I am just now going through my wife’s jewellery box to test the scenarios… I’m having trouble finding a brooch, unfortunately, so might be stuck until Sunday afternoon at my mother’s house.

27. Rod Kimball says:

The part where she’s wearing only two bits of jewelry took me about 10 seconds. I’m curious about those who say the whole thing took < 5 seconds. On Monday, please tell me how you did it.

It is nice that our Mr. spoiler has about as much chance of actually spoiling a puzzle as a box of rocks.

28. Very easy one this week. Unless I missed a trap.

29. Anonymous says:

Very easy one this week

30. Douglas Anderson says:

Ooops, went slightly off-track. Still only took 10 seconds (even with a really very silly initial mistake. Nice easy one for a Friday!

31. happy day says:

For those wondering why not wearing any jewelry isn’t included and not joking:
If we were asked ”what are the different results if we flipped a coin 1 time, the answer would be 2 possibilites (heads or tails) not 3 possibilites (heads, tails, or not flip the coin). Not wearing any of the 4 jewelry items is comparable to not flipping a coin and would be wrong. The problem said “how many combinations of her jewelry does she have to choose from” So you have to choose/pick/include one or more pieces of the jewelry. But if someone wants to include not wearing anything, it’s easy to just add
one extra outcome.

Regarding Barry g-ODD-ard. If it is one individual and not others playing around, he
illustrates he isn’t very bright, if he thinks the answer is 4 factorial and doesn’t realize that answer would be wrong/overstated due to repetitions. In other words, If a person eats an apple + orange, it is the same combination as eating an orange + apple. Or if a person wears a ring + bracelet it is the same as wearing a bracelet + ring.

• Eddie says:

I’m afraid you’ve mixed up permutations and combinations.

Reminds me – an chinese guy once used the word ‘interputation’ on an in-house discussion group – which made me laugh. A very logical kind of interpretation.

• The other Matt says:

Good idea, to think about that too. But, from which number up we talk about a “combination” ? One, or two ?
So if we think further that way, we have to define that first.

32. Peter says:

None.
Probably doesn’t match any of her clothes.

33. Anonymous says:

I’m surprised Pascal hasn’t been mentioned

34. Mervulon says:

You’re collective bickering is so boring, I’m just out of here. And it’s your loss. Not that i expect you to get that.

35. Shenahn@aol.com says:

____________________________________

36. About a minute – using pen, paper and WolframAlpha 🙂

37. I came up with 256. Oops! Not suppose to

38. Alex says:

I write Python program to calculate. Given 1 – a ring, 2 – a necklace, 3 – a bracelet and 4 – a brooch.
The program gives this result: [1, 2, 3, 4, 12, 13, 14, 23, 24, 34, 123, 124, 134, 234, 1234], i.e 15 combinations in 15 seconds.
If there will be 3 pieces of jewelry results are [1, 2, 3, 12, 13, 23, 123] i.e 7 combinations in 3 seconds.
If there will be 5 pieces of jewelry results are [1, 2, 3, 4, 5, 12, 13, 14, 15, 23, 24, 25, 34, 35, 45, 123, 124, 125, 134, 135, 145, 234, 235, 245, 345, 1234, 1235, 1245, 1345, 2345, 12345], i.e 31 combinations in 61 seconds.
I spend 1.5 hours to write the program.
Tomorrow I will post solution for 6 pieces of jewelry

• Alex says:

If there will be 6 pieces of jewelry results are
[1, 2, 3, 4, 5, 6, 12, 13, 14, 15, 16, 23, 24, 25, 26, 34, 35, 36, 45, 46, 56, 123, 124, 125, 126, 134, 135, 136, 145, 146, 156, 234, 235, 236, 245, 246, 256, 345, 346, 356, 456, 1234, 1235, 1236, 1245, 1246, 1256, 1345, 1346, 1356, 1456, 2345, 2346, 2356, 2456, 3456, 12345, 12346, 12356, 12456, 13456, 23456, 123456], i.e 63 combinations in 201 seconds.

39. what about the combo of “none” 🙂