Will they fit? – 2
I just got a 1 0 × 1 0 -piece jigsaw puzzle. All of the pieces only fit together one way. Each piece connects to at least two other pieces.
My assembly plan: I'm going to take pieces from the box one by one at random , and fit them together if possible. I'll keep going until all of the pieces taken out fit together in one connected clump .
If I've already taken out two pieces that don't directly connect, what is the maximum number of additional pieces that I might need to draw in order to connect them?
The answer is 97.
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4 solutions
36 total prices already taken from the box + 99 peices to draw = 135. This problem is incorrect because you can't draw 135 pieces from a box that only contains 100
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Where did you see 133? The solution is 97 which is what all solution writers say.
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I see him saying 36 + 99 = 135. You ask where he sees 133, so I'm assuming that at first he typed 36 + 97 = 133 (no idea why it was edited like that). My guess is that the 36 are the two unconnected pieces plus the 34 connected pieces from the image that is shown. If next you draw 97 new pieces as per the answer, you get 2 + 34 + 97 = 133 in total.
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@Carlo Wood – Ahh, I see. Indeed, he first said 133, which probably comes from 97 (answer) + 34 (picture) + 2 (text). But know, I don't know where he gets 99 fom.
I'm sorry, I don't understand where you got 133 from.
If we start from beginning, if we pickup 51 pieces, 2 of them must connect. So answer should be 49. Unless I am going to match with first picked up piece.
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The problem asks for the number of pieces so that all pieces connect, not just two.
I miss read the puzzle, solved a completely different puzzle and still had it "right", heheh.
Perhaps I misread it or the information was not detailed enough. Each piece connects to at least two other pieces. Does this mean the pieces can connect to all the pieces?
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It's a normal square puzzle, so each piece connects to either 2, 3 or 4 neighbouring pieces.
Where do you see these "details and assumptions"? I don't see anywhere in the problem where it says that pieces joined by a corner don't count.
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The wording has been changed and now this is implied in the phrase connected clump .
I thought we only needed to connect the original two jigsaws displayed in the picture and f the rest!?
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It says "until all of the pieces taken out fit together in one connected clump."
There are a total of a 100 peaces 2 of which are removed from the box. This leaves 98 in the box. Since one connector peace is sufficient for a connection, you are essentially looking for 1 in 98. The maximum number to draw would corespond to you being so unlucky that you you pick 97 peaces and none of them connected the peaces you have. At this point you found the connector peace by inference but in order to actually connect them you would have draw that 98th peace as well
"Them" should be specified. Because it could mean: 1. all of them 2. The two picked at the beginning 3. Any of them
Answers would be; 1. 97 (2 + 97 = 99) 2. 97 (2 + 97 = 99) 3. 49 (2 + 49 = 51)
Problem not explicitly defined
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Comment not explicitly defined. What exactly did you misunderstand?
I understand your solution but there is one line stating that one of the pieces has already been taken out therefore Additional number of pieces must be 97-1=96
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The problem states that two pieces have been removed. 99 pieces total must be removed to ensure that each square is connected, so 99 - 2 = 97.
Funny to see how everybody writes "piece" in his own way. I found also the problem poorly defined.
I for some reason thought that the question was the minimum amount needed in the worst case scenario and got 17...
96 isn't enough: I could be so unlucky to pick a corner piece but miss its two neighbours. I need 2 + 9 7 = 9 9 to be sure that I have picked a neighbour of each piece.
The question is a little confusing. "Every piece is equally likely to be picked" is a red herring if the sought answer is the worst case scenario regardless of its likelihood.
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With that I wanted to make sure that there are no tricks like picking an edge piece after having chosen a corner (when drawing pieces from a pile you can see whether they have a straight edge), but actually you're right. The worst case scenario stays the same as long as there is no method that guarantees to pick the right pieces.
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Actually, after thinking a little bit more, I realised that this strategy can help reducing the number of pieces required.
By first picking all edge and corner pieces, one can prevent the worst case scenario from happening and reduce the number of required pieces down to 9 3 .
I was very confused by the wording of the question. It was not clear whether each time a piece is taken out of the box, that piece is tried against all previous pieces drawn, just the original two pieces drawn, or just the first piece drawn. Also, it was not clear what was meant by "in order to connect them". Does this mean connect all the pieces of the puzzle? If so, then you would need to draw every piece from the box and the solution would be trivial. Does it mean to connect a piece to both of the two original pieces? Or one of the original two pieces? Does it mean to connect at least two of all the pieces drawn so far? (This was my interpretation, and I actually think it is a more interesting question.) Does it mean to connect all the pieces drawn so far? (Turns out this appears to be what was meant, but this interpretation didn't even occur to me reading the question.)
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In the case of your question, I believe the answer is 50 (the pieces create a checkerboard pattern).
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Yes, you’d have to draw 51 to guarantee at least one fit, minus the 2 already drawn, that means 49 more from the question’s starting point. This assumes the pieces are shaped in a grid with each piece other than edges and corners having 4 neighbors. Not necessarily square or even rectangular. Depending on shape of pieces you could have a trapezoid or other irregular shapes.
I find the "assembly plan" quite clear: "I'm going to take pieces from the box one by one at random, and fit them together if possible. I'll keep going until all of the pieces taken out fit together in one connected clump." Do you have any concrete suggestions on how this wording could be improved?
I gave '98' as an answer just in case the size of the puzzle is 1x100.
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Me as well! They should add the restriction that the jigsaw is a rectangle that doesn't have dimensions 1x100.
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Brilliant Brilliant! They have updated and stated the puzzle size is 10x10 now.
Nice try, but it states every piece connects to two other pieces, so the puzzle can't be 1x100.
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That restriction was updated after this complaint ;)
What confused me was the word 'clump' and the arrangement example that seemed like a random, nucleated mess, when they were all actually in their exclusive places in the grid. (Yes, there were edges that lined up, but they didn't seem significant.) That led me to think "All of the pieces only fit together one way" as a more lenient constraint, as in male to female connections instead of unique locks and keys, so I ended up overcomplicating the process. Maybe calling it an 'incomplete solve' would have made it easier to see that, but it's hard to tell in hindsight.
I was working with reference to the "clump" shown in the picture. Poorly worded and described Grr!
If one of the starting pieces is a corner piece, drawing 9 6 more pieces may miss the 2 pieces adjacent to the corner piece, but drawing 9 7 more pieces guarantees one connected clump .
Technically, the puzzle does not even need to be a rectangle according to the problem.
Author: chrisyatesstudios
https://commons.wikimedia.org/wiki/File:Ignis-spindle-fin12.jpg
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But it is stated that it is a 1 0 × 1 0 puzzle
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It has now been updated.
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@Zain Majumder – My solution has now been updated.
Is that picture a cake because it looks delicious 😂 but the wording is this question was confusing. How was I supposed to know the size of each piece..? They said the puzzle was 10 by 10 however the pieces could have varied in size thus meaning there was less than 100 pieces. Right?
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Or even more than 100 pieces....
I think that, as long as nothing is said about the pieces explicitly, you can assume the simplest arrangement, which is just 1×1 squares
I found the question vague. If I have selected 2 pieces at the start, am I to assume these pieces fit together ? Are we throwing these pieces back in the box and selecting 2 more random pieces ? There is no guarantee that we will ever randomly pick a single piece that may be needed to grow the clump, unless we're putting selected pieces into a different pile
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It is stated that
- I've already taken out two pieces that don't directly connect
- the maximum number of additional pieces
- I'll keep going until all of the pieces taken out fit together in one connected clump.
It actually boils down to the fact that NO-ONE had carefully read the rules! "If I've ALREADY TAKEN OUT TWO pieces that don't directly connect, what is the maximum NUMBER OF ADDITIONAL PIECES?" So - if that unlucky person took the pieces of the directly opposite diagonal corners, or like in this solution picture - anything else + 1 exactly in the corner, then we come to the point that we see on that picture by this math: 10x10=100; 100-2(already taken out)=98; 98-2(missing)=96 and then we yet need another one to finally connect 96+1(to finally connect)=97!
At first I thought the answer was 98, because there is only one piece in the box that will directly connect the original two pieces, so you might have to draw every piece in order to find it. That would be 98 pieces drawn. But, if you draw every piece except the one piece that goes directly between the two original you still connect the two as part of the bigger clump. So you've drawn 97 pieces, everything connects, and the only piece not drawn is the one that goes between the first two pieces.
Consider the case that looks somewhat like this:
Since it is specified in details and assumptions that pieces joined by only a corner do not count, we must draw one more piece to place in one of the empty squares, to ensure that each square is connected to the main puzzle. This would mean that the total number of pieces that must be drawn is 2 + 9 7 = 9 9 .