How do you play The Jigsaw Puzzle Game?

1. Introduction and needed items

This game was first thought of around Mar 13, 2005. Since I first came up with the concept, I haven't changed it except with the addition of one minor new rule allowing for bonus points.

This game doesn't require much:

1 jigsaw puzzle (any size and any number of pieces is acceptable)
1 piece of paper
1 pencil or pen
1 calculator (optional)

This game doesn't require any setup, just a spot to put the puzzle on.

2. How to play

To play the game, you just put the jigsaw puzzle together. Each time you insert a piece, you score points, whether it's part of the main frame or just two pieces that get linked together. In short, you score 1 point if you insert one piece into the frame or another group. For anything bigger inserted, such as a group of 5, you'll score "n(n+1)/2" points. When you insert groups, you score for the smallest one. That is, if you have a group of 3 and a group of 5 and pick up the group of 5 and insert it into the group of 3, you'll get credit for the group of 3 giving you 6 points. When combining groups of groups, remember that you'll only score based on the smallest group. For example, if you have a group of 7, 5, and 3, you can score the most points if you merge the groups of 3 and 5 (scoring 6 points) to form a group of 8 then merge this group of 8 with the group of 7 (scoring 21 points). If this will fit into the main frame, as long as it has greater than or equal to 15 pieces, you'll score 120 points for merging it. The bigger your groups get, the more powerful the effect gets as you insert single pieces, however, it no longer is effective at all if your group exceeds the largest group. For example, if your main frame (the one with all the border pieces and stuff) consisted of 90 pieces and you formed your group to have 135 pieces, you'll only get credit for the 90. Even if you know exactly where the group goes, you can still extend onto it for more points. You only score when you insert the group into another.

Here's a chart for the first 100 group sizes to help you out. If you get anything bigger, just use the formula "n(n+1)/2" to find your score where n is the number of pieces in the smallest group.

Quick scoring reference chart
n	score	n	score	n	score	n	score	n	score
1	1	21	231	41	861	61	1891	81	3321
2	3	22	253	42	903	62	1953	82	3403
3	6	23	276	43	946	63	2016	83	3486
4	10	24	300	44	990	64	2080	84	3570
5	15	25	325	45	1035	65	2145	85	3655
6	21	26	351	46	1081	66	2211	86	3741
7	28	27	378	47	1128	67	2278	87	3828
8	36	28	406	48	1176	68	2346	88	3916
9	45	29	435	49	1225	69	2415	89	4005
10	55	30	465	50	1275	70	2485	90	4095
11	66	31	496	51	1326	71	2556	91	4186
12	78	32	528	52	1378	72	2628	92	4278
13	91	33	561	53	1431	73	2701	93	4371
14	105	34	595	54	1485	74	2775	94	4465
15	120	35	630	55	1540	75	2850	95	4560
16	136	36	666	56	1596	76	2926	96	4656
17	153	37	703	57	1653	77	3003	97	4753
18	171	38	741	58	1711	78	3081	98	4851
19	190	39	780	59	1770	79	3160	99	4950
20	210	40	820	60	1830	80	3240	100	5050

If you look at the chart carefully, you'll notice a few patterns. Where n is 1, you score 1 point. Where n is 2, you score 3 points, two more than before. Where n is 3, you score 6 points, 3 more than before. Where n is 4, you score 10 points, 4 more than before. Do you notice the pattern?

3. How to win

3.1 Highest score mode

First, you must set a goal before starting the puzzle. The goal is dependent on the maximum possible score for your puzzle. For a babyish game (in terms of difficulty), you should target 5% of the maximum score. For an easy game, you should target 10% of the maximum score. For a medium game, you should target 15% of the maximum score. For a hard game, you should target 20% of the maximum score. For a extreme game, you should target 25% of the maximum score. Calculating the maximum possible score is very time consuming and the more pieces the puzzle has, the longer it takes to calculate. This table below includes the maximum possible scores for each of the common puzzle sizes. Find the puzzle size you have and your target difficulty. To win, you must score more points than what is on the table.

Maximum scores and targets
Number of pieces^*	Maximum score	Baby 5%	Easy 10%	Medium 15%	Hard 20%	Extreme 25%
100	2703	135.15	270.3	405.45	540.6	675.75
200	7753	387.65	775.3	1162.95	1550.6	1938.25
300	23229	1161.45	2322.9	3484.35	4645.8	5807.25
400	27853	1392.65	2785.3	4177.95	5570.6	6963.25
500	63789	3189.45	6378.9	9568.35	12757.8	15947.25
750	142697	7134.85	14269.7	21404.55	28539.4	35674.25
1000	189039	9451.95	18903.9	28355.85	37807.8	47259.75
1200	248679	12433.95	24867.9	37301.85	49735.8	62169.75
1500	424322	21216.1	42432.2	63648.3	84864.4	106080.5
2000	689539	34476.95	68953.9	103430.85	137907.8	172384.75
3000	1550072	77503.6	155007.2	232510.8	310014.4	387518
4000	2690539	134526.95	269053.9	403580.85	538107.8	672634.75
5000	6267252	313362.6	626725.2	940087.8	1253450.4	1566813
6000	6051572	302578.6	605157.2	907735.8	1210314.4	1512893
8000	10692539	534626.95	1069253.9	1603880.85	2138507.8	2673134.75
10000	18769752	938487.6	1876975.2	2815462.8	3753950.4	4692438
12000	24054572	1202728.6	2405457.2	3608185.8	4810914.4	6013643
18000^**	81069796	4053489.8	8106979.6	12160469.4	16213959.2	20267449

Table footnotes:
* If you see another sized puzzle not on this chart, E-mail me and I'll insert it into the chart. I covered as much as I could, except baby puzzles. There is no formula for calculating it, the process is rather complicated^*.
** 18,000 pieces is the world's largest puzzle available. These are so big that they can fit 2/3 of a standard 11.5 by 11.5 foot room.

3.2 Lowest score mode

This is the main version. There's a second version to this game as well. Instead of going for the highest possible score, you need to go for the lowest possible. Unlike the highest possible, it's extremely easy to distinguish what the lowest possible is. Because it takes two pieces to score one point, and each additional piece after that as one point, the lowest possible score is the same as the number of pieces in the puzzle minus one. For example, a 500-piece puzzle would have a minimum of 499 points. This table below shows you the scores you need to win using low score mode. Find the puzzle size you have and your target difficulty. To win, you must score below what is shown on the table.

Minimum scores and targets
Number of pieces	Minimum score	Baby 300%	Easy 250%	Medium 200%	Hard 150%	Extreme 125%
100	99	300	250	200	150	125
200	199	600	500	400	300	250
300	299	900	750	600	450	375
400	399	1200	1000	800	600	500
500	499	1500	1250	1000	750	625
750	749	2250	1875	1500	1125	937.5
1000	999	3000	2500	2000	1500	1250
1200	1199	3600	3000	2400	1800	1500
1500	1499	4500	3750	3000	2250	1875
2000	1999	6000	5000	4000	3000	2500
3000	2999	9000	7500	6000	4500	3750
4000	3999	12000	10000	8000	6000	5000
5000	4999	15000	12500	10000	7500	6250
6000	5999	18000	15000	12000	9000	7500
8000	7999	24000	20000	16000	12000	10000
10000	9999	30000	25000	20000	15000	12500
12000	11999	36000	30000	24000	18000	15000
18000	17999	54000	45000	36000	27000	22500

4 Multiplayer

If you want some competition, you can certainly have some. If you plan on having competition, you may, optionally, set a time limit. You will, however, need to monitor the time you spend regardless on what you're doing. Also, all players/teams must have the exact same puzzle. If you decide on having competition, first, decide on whether or not you want a time limit. Second, decide on which puzzle you wish to use (both must be exactly identical: picture, piece shapes, and number of pieces). Finally, decide on which mode you want to play with (whether for highest or lowest score). For competition, I wouldn't recommend going much above 300 pieces. Once that's agreed upon, have the players/teams separated either by significant distance (like 10 feet or more) or have a barrier between each other so no one can see each other's progress.

The winner of the highest score mode is the player/team with the highest score. The winner of the lowest score mode is the player/team with the lowest score. If there happens to be a tie (more common with smaller puzzles on the low score mode), the player/team with the fastest finish time wins.

If you only have one of a specific puzzle and don't want to buy another copy of it (especially if it's an expensive one), an alternative is to let one player/team work the puzzle and score his/her points. The other player/team cannot watch over them. When that player gets done with their game, they'll need to write their final score on a sheet of paper and put it in an envelope or secure it. Then, the puzzle must be broken up into it's pieces again and the next team must go as well. The winner is determined in the same fashion.

**************Add dream about trying to sleep in basement with about 5 tornadoes swifting side by side outside****************** Footnotes:
* The process to computing the maximum possible score involves a bit of logic and problem solving, mainly working backwards. You start with the full puzzle. Then, you cut it in half continually. If you end up with something like a group of 25, it gets broken up into a group of 12 and 13. Here's the math behind the 100-piece puzzle's maximum score.

math	notes about this step
100	Your base; 100 breaks into 2 groups of 50;
2@50 = 1275	Merging 2 50's gives 1275 points; 2 50's break inot 4 25's;
4@25 = 650	at 325 points each, you're merging 4 25's into 2 sets of 50 so you score double; 4 25's breaks into 4 12's and 4 13's;
4@12+4@13 = 78+91	Merging a 12 with a 13 gives credit only for the 13; merging the 13's gives more points; 2 scores at 12 and 2 scores at 13 gives 78+91 or 169 points
8@6+4@6+4@7 = 12@6+4@7 = 126+56	breaking the 4 12's gives 8 6's and the 4 13's into 4 6's and 4 7's; having 8 6's and 4 6's is the same as having 12 6's; 6 scores at 6 gives 126 points and 2 scores at 7 gives 56 points totalling 182;
24@3+4@3+4@4 = 28@3+4@4 = 84+20	breaking the 12 6's gives 24 3's and the 4 7's gives 4 3's and 4 4's totalling 28 3's and 4 4's; 14 scores at 3 gives 84 points and 2 scores at 10 gives 20 points totalling 104;
28@1+28@2+8@2 = 28@1+36@2 = 28+54	28 3's gives 28 1's and 28 2's and 4 4's gives 8 2's totalling 28 1's and 36 2's; 28 scores at 1 gives 28 points and 36 scores at 2 gives 54 points totalling 80;
72@1 = 72	Because 1's cannot be broken up any further, you can remove them from the list; 36 2's breaks into 72 1's giving 72 points;

The final step is to add up the scores from these which should total 2703 points. The process is rather easy to understand, it's just very time consuming and a calculator is highly recommended. If the puzzle has an odd number of pieces, such as 1035, it'll break up into a group of 517 and 518. You score for the 517. Then, from there, you just continually break it down. The more pieces the puzzle has, the more steps are required to get the answer.

To check your answer, the best way to do it is to add up your 1's. In the example above, you had 28 1's which got removed then 72 ones following that. 28+72 make 100. Another way to check, while in the process of calculating it is to add up your groups. For example, on the like where it starts 24@3, add up the sets of groups. 24+4+4 makes 32, which is a power of 2. The next line below that should add up to 64. The line above it should add up to 16. This is the easiest way to check your work both at the end in while in progress.