P=NP (iOS)

• How to play
• Interface
• Score

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How to play

1. Download the game for free on your iPhone or your iPad ( > here < ).
2. Launch the game.
3. Do as you are told during the tutorial and everything will be all right. If you are a rebel at heart, you can quit the tutorial from the pause menu. The tutorial can be replayed anytime from the main menu.
4. From the main menu, select how many dots you wish to play with using the plus (+) and minus (−) buttons. You can select as few as 3 dots and up to 35 dots.
5. Choose a puzzle in the list. The difficulty increases probabilistically as you approach Z. The random puzzle, marked with a star (*), will unlock once you have completed all puzzles from A to Z of the same level, and allow you to play a different puzzle each time. In the random puzzle, both the placement of the dots and the difficulty are random.
6. Once the game has started, all the dots you have to link together are displayed. The distance to be covered (aka the target), in pixels, is displayed at the very top of the screen. Touch the dots to connect or disconnect them. Your current distance is displayed just under the target in the HUD. Do not forget that the world wraps both horizontally and vertically; a dot located at the very right of the screen, for example, is in fact really close horizontally to a dot located at the very left of the screen. Slide your finger on the screen to move the dots and thus make it possible to connect them optimally. You have to connect all the dots and come back to where you started. The starting dot, in yellow brackets, becomes available again only once all other dots are connected.
7. Should you not have found the best route on your first try, your best route will be represented as a dotted line. Your best distance is displayed just under the current distance in the HUD. You can choose to display as a dotted line either your best route or your previous route. You can also hide the dotted line by touching the eye icon in the controls.
8. If you are stuck, you can use a hint. To do so, touch the magnifier icon at the bottom right of the screen. The number at the bottom right of the magnifying glass indicates how many hints are left. Win hints by completing puzzles or buy them directly in the in-app shop. Hints are available as soon as you have completed a first route and highlight the good parts of your best attempt. If no segment of your best route is highlighted after using a hint, it means none are correct! A hint remains available until you improve your best route.

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Interface

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Score

Completing a puzzle rewards you with points that are traded automatically with hints. You win a hint every 10000 points. The score is calculated as follows:

• Puzzle completed
  You are awarded 10 points for having completed the puzzle.
• Level bonus
  You are awarded additional points depending on the number of dots (level) of the puzzle. They are distributed as follows:

  Level	Points
  3	0
  4	9
  5	39
  6	87
  7	156
  8	243
  9	351
  10	478
  11	624
  12	790
  13	975
  14	1180
  15	1404
  16	1648
  17	1912
  18	2195
  19	2497
  20	2819
  21	3160
  22	3521
  23	3902
  24	4302
  25	4721
  26	5160
  27	5619
  28	6097
  29	6594
  30	7112
  31	7648
  32	8204
  33	8780
  34	9375
  35	9990

• Difficulty
  Type: multiplier
  Minimum value: 0.59
  Maximum value: 1.41
  Independant from your performance, this multiplier represents the difficulty of the puzzle. You earn more points for completing more difficult puzzles.
• Time
  Type: multiplier
  Minimum value: 1.00
  Maximum value: 1.41
  This multiplier rewards fast players. Those who prefer a slower pace are not penalized, since its value is always greater than or equal to 1.
• No hint used
  Type: multiplier
  Minimum value: 0.1 (at least one hint used)
  Maximum value: 1.0 (no hint used)
  If you use a hint, you will earn only 10% of the points you could have earned without using a hint, assuming a constant completion time.
• Replay
  Type: multiplier
  Minimum value: 0 (the puzzle had already been completed)
  Maximum value: 1 (the puzzle had never been completed)
  Thus no point is awarded if the puzzle had already been completed. Only apply to A-Z puzzles. Regarding the random puzzle (*), it is always assumed that it had never been completed before.
• Total
  Total number of points awarded.
  
  Total = (Puzzle completed + Level bonus) × Difficulty × Time × No hint used × Replay
• Previous balance
  Current number of points before completion of the puzzle.
• Hints awarded
  Points traded with hints, if any. Its value is negative or zero and is a multiple of 10000.
  
  Hints awarded = −10000 × ⌊(Previous balance + Total) / 10000⌋
• New balance
  Remaining points after deduction of the points traded with hints. The new balance is thus always inferior to 10000.
  
  New balance = Previous balance + Total + Hints awarded

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