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I have a number of old 1000-piece jigsaw puzzles I'd like to sell. I'd like to make sure they are complete first. Is there a faster way to determine whether there are exactly 1000 jigsaw pieces than physically picking up and counting every single one of them?

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Count by 5s. That's about the best you can do. Separate them into groups of the same size and count one group, and count how many groups you have. –  Craig Oct 13 '11 at 13:37
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I'd go by 10s instead. Form a cube of pieces. Unless they're bent you can easily check that the piles are the same height, so you don't need to worry about losing count. –  Peter Taylor Oct 13 '11 at 14:03
    
You only have to count the pieces of the first puzzle. For the others a one-one match would do. –  Christian Blatter Oct 13 '11 at 14:52
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The old $1000$-piece jigsaw puzzles in my home cannot be tested for completeness by mere counting. Alas, my children have on occasion mixed up pieces from different puzzles, and having $1000$ pieces in a box does not guarantee that the puzzle is complete. –  Dilip Sarwate Oct 13 '11 at 16:39

5 Answers 5

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I don't know of one. To know the number you should have (it may not be exactly 1000), you can assemble the border. Many puzzles are cut with a rectangular grid and you can multiply the number of rows by the number of columns. Unfortunately, I have also seen a number where the grid is perturbed in a small region of the center and the count is changed by 1 or 2.

With an accurate scale, if you have more than one puzzle in the same series, you could weigh the pieces. The thickness and outer dimensions will be nominally the same. Whether they are controlled within 0.1%, however, may be questionable.

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1000-piece jigsaws don't even have exactly 1000 pieces? Ugh. Well I'm glad I found this out before I started counting. That may take figuring out if a puzzle is complete without actually assembling it from daunting to impossible. D: –  Emaille Oct 13 '11 at 14:03
    
@Emaille: No, I multiplied up some of the 500 piece ones that were cut rectangular years ago. It was always a little higher than 500. –  Ross Millikan Oct 13 '11 at 14:16
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If puzzles are cut on a rectangular grid, then, assuming that the ratio of the puzzle dimensions is $4:3$, one might expect a "$1000$-piece puzzle" to have $28$ rows, $36$ columns, and $36\times 28 = 1008$ pieces. –  Dilip Sarwate Oct 13 '11 at 16:54

Note: While the thread may have long served it's purpose, I am proposing the following for archival purpose.

You can take a photo after scattering them on a white background and use any software that uses thermal imaging to count, or use infrared beam by having them slide in a narrow strip at an angle that will interfere with the light registering a 'tick'.

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I once treid once piece on a digital scale, then weighing the lot, however I don't deem this to be a very accurate way of doing it.

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Why not take 50 random pieces , measure the weight of them, multiply by 20, and if the weight is inside interval [weight_of_50*20-smallest_piece,weight_of_50*20+smallest_piece] you're good. Is that a reasonable approximation? Of course, you need to have an accurate scale for this. –  enedene Oct 13 '11 at 14:00

The only way you can guarantee the jigsaw is complete is to physically do the jigsaw.

Some jigsaws, particularly, Waddingtons & Tower Press jigsaws, have pieces with five connectors so even if you do the border and count the rest, you're not certain it's complete.

For example; some 500 pieced ones may have 502 pieces even the border is 20 x 26 pieces (520), some 750s have 750 pieces even though the border is 24 x 32 (768).

You could also have the other extreme where some pieces are in two bits some 1000 pieced. Some Waddingtons/Tower press ones have this setup with the border 38 x 26 (988).

Any jigsaws with whimsies will also be tricky in relation to 'just doing the border' pieces.

As I've said, earlier, best do the jigsaw, to be certain.

Good luck. :)

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Try to stack them in a 10x10x10 cube

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