Solve a problem here and prove urself.. :afrog:

Suppose you have, say, a stone tablet of some sort. The tablet has 16 pieces missing. But lucky you, you have the pieces! You can tell by looking at the pieces which ones are the four corners, which ones are the eight side pieces, and which ones are the inside pieces. Otherwise, you can't tell where on the tablet they should go or how they should be oriented.

If it takes 90 seconds to place all of the pieces, how many days will it take to try every possible combination? Please round to the nearest full day.
Answer will be posted only if at least five people gives up

My first (educated) guess is 1548288 days.

24,192 days?

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Originally Posted by sinnerFA

24,192 days?

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I think this is the result if you don't take into account that every piece can be placed in 4 different orientations.

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Originally Posted by Me

My first (educated) guess is 1548288 days.

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I think this was far too optimistic. The fact that each piece has 4 possible orientations considerably increases the possibilities. My second guess is about 1.2*10⁵⁹ days, just the time to snap your fingers!

103903848824832 days?

There are 4^4 = 256 arrangements possible for the corners, the same for the inside pieces and there are 4^8 = 65,536 arrangements possible for the side pieces. That sums up 66,048 arrangements which means 69 days altogether. Right?

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Originally Posted by [Pieter]

103903848824832 days?

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I agree with you (my third guess already)

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Originally Posted by Rassis

There are 4^4 = 256 arrangements possible for the corners, the same for the inside pieces and there are 4^8 = 65,536 arrangements possible for the side pieces. That sums up 66,048 arrangements which means 69 days altogether. Right?

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You have to multiply these numbers. And aside from the 4 possible orientations of each piece, all possible permutations (different places for the pieces) must be taken into account. I think it's like this:

Corners: 4! * 4⁴
Sides: 8! * 4⁸
Inside: 4! * 4⁴

and the total number:

N = 4! * 4⁴ * 8! * 4⁸ * 4! * 4⁴ = 9.974769*10¹⁶

So that the number of days will be N * 90 / 60 / 60 / 24 and the result is what [Pieter] has posted above.

Krtxmrtz,
I see your point and I agree except...
...if corners, sides and insides form three independent sets (each one composed by all possible arrangements: corners = 4!*4^4, sides = 8!*4^8 and insides = 4!*4^4) why to multiply the results? To sum them up makes more sense to me, unless you consider also permutations of the three sets - which was not clear in the question. The final result would thus be 2.752.525 days.

I'd say <900 seconds. Once you got the corners or the sides, there would only be the center to manipulate. A 16 piece puzzle won't take more than an hour, usually.

dglienna,

Your answer shouldn´t be the result of a gut feeling only. Take into consideration the whole text in the question and I (and certainly everybody) will be happy if you try again.

Well, if you can't see the answer right off the bat, then any piece could go into any position, so I'd figure it like this:

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20922789888000 16!

/ 86400 sec/day
960 chances/per day

21794572800 days

to try every combination

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Quote:

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Originally Posted by Rassis

...if corners, sides and insides form three independent sets (each one composed by all possible arrangements: corners = 4!*4^4, sides = 8!*4^8 and insides = 4!*4^4) why to multiply the results?

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They are not independent sets for you look at the entire jigsaw as a whole. For example, for a certain arrangement of the corners you have all possible arrangements of the sides. Then for a different arrangement of the corners you again have all the possible arrangements of the sides. That's why you must multiply.

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Originally Posted by krtxmrtz

They are not independent sets for you look at the entire jigsaw as a whole. For example, for a certain arrangement of the corners you have all possible arrangements of the sides. Then for a different arrangement of the corners you again have all the possible arrangements of the sides. That's why you must multiply.

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I agree. Thanks.

I've been concentrating on this for a while and I'd bet my boots on [Pieter]'s answer.

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Originally Posted by [Pieter]

103903848824832 days?

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I got very close to this.

My answer is a bit larger... it's been forever since permutations, and that was 7th grade so here goes:

These assume that by being able to determine what each piece is, you can tell which side(s) are edges. Ex. a corner piece has these two edges [given], and an edge piece has this one edge [given].

Corner pieces:
Each corner piece may only be placed in 4 spots, and the orientation does not affect anything since there is only one orientation per piece per spot. So, the number of combinations of corner pieces is 4 nPr 4 = 4!

Edges:
Each edge piece may be placed in any of 8 spots, and the orientation does not matter as each piece can only be placed in each spot in one way. So, the number of combinations of edge pieces is 8 nPr 8 = 8!

Middle:
The large number. Each middle piece may not only be placed in one of 4 spaces, but also may be placed in four different orientations per place, so the number of combinations of middle pieces is (4*4) nPr 8 = 16!/8!.


The total number of combinations would then be 4!8!16!/8! = 16!4! or 24*16!, a number that would equal 502146957312000, or 523069747200 days.

Note: Edited to use 4 middle pieces instead of 8. Made it a bit smaller :)

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You can tell by looking at the pieces which ones are the four corners, which ones are the eight side pieces, and which ones are the inside pieces. Otherwise, you can't tell where on the tablet they should go or how they should be oriented

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Each Peice also has 2 more orientations, "Face Up" and "Face Down".

Now, I don't think you should be counting all the permutations, just the combinations.

UL-UR-LR-LL: 1234 and UL-UR-LR-LL: 4123 are the same thing. I would not put it together more than once. Just once, then "walk around the table".

:)

Hmmm.
The Outer Corners and the Inner peices are, i assume, squareish.

However, are the eight outside peices squarish or rectangularish?

:wave:

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Originally Posted by anarchy.spirit

If it takes 90 seconds to place all of the pieces, how many days will it take to try every possible combination? Please round to the nearest full day.

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So we don't count the impossible combinations?

So if there is only 1 possible combination that the tablet can be correctly put back together with, then I guess the answer is 0 days.

1.1998852139365e+59

OK, let's settle this once and for all. Would anyone just volunteer to try out all the possibilities and keep a tally? :D