Levels

Connect the Dots:  Portals features 10 level packs each with 150 levels. 

The packs follow two main types – one based on the number of portals and the other based on the size of the board. 

 

The following table shows the number of levels with 1-6 portals in each pack: 

Pack	1	2	3	4	5	6	Avg
The Beginning	150	0	0	0	0	0	1
Double Trouble	0	150	0	0	0	0	2
Tripping Out	0	0	150	0	0	0	3
Fives	59	64	23	4	0	0	1.81
Sixes	27	69	38	16	0	0	2.29
Sevens	9	41	64	36	0	0	2.85
Eights	5	30	54	40	17	4	3.31
Nines	0	20	47	50	26	7	3.69
Crazy Quads	0	0	0	150	0	0	4
Space	0	75	75	0	0	0	2.5
Time	0	0	0	35	79	36	5.01

The next table shows the Average Tiles, Pairs of Dots, Line Length, Portals, and Tiles/Portal for each pack: 

Pack	Tiles	Dots	LineLen	Portals	T/Port
The Beginning	72.1	6.97	10.06	1	36.1
Double Trouble	102.0	7.98	12.28	2	25.5
Tripping Out	117.6	8.34	13.38	3	19.6
Fives	70.0	6.19	10.72	1.81	19.3
Sixes	96.0	7.68	11.9	2.29	21.0
Sevens	126.0	8.77	13.71	2.85	22.1
Eights	160.0	9.93	15.45	3.31	24.2
Nines	198.0	11.74	16.24	3.69	26.9
Crazy Quads	145.2	9.77	14.05	4	18.2
Space	195.6	9.17	20.71	2.5	39.1
Time	195.6	11.45	16.21	5.01	19.6

T/Port = Tiles per portal.  Note that each portal covers 2 tiles.  

The first 3 packs have a consistent number of portals per level – with the portals starting at 1 per level in The Beginning and increasing to 3 per level in Tripping Out (The Crazy Portal details much a difference this makes in the levels). 

The following 5 packs are named for the board size (specifically, the height of the board):  Fives, Sixes, Sevens, Eights, and Nines.  The number of portals is “random” for these packs, though the as the board size increases so does the average number of portals.   The average number of portals doesn’t pass the 3 portals in Tripping Out until you reach Eights. 

Crazy Quads picks off where Tripping Out left off.  The board sizes are actually smaller than those in Eights and Nines despite having more portals.   It’s 18.2 tiles per portal is the highest portal density in the game.

Space is the new level pack although 2nd to last in the order.  More detail on Space below. 

Time (formerly called “Insanity”) is the final pack in the game, and features large boards with 4-6 portals.  

Level Groups

The 150 levels in each pack are divided into 5 groups of 30 levels, with the board size increasing every 30 levels.  

Fives through Nines

Each of these packs starts out with square shaped boards (5x5x2 for Fives, 6x6x2 for Sixes, etc).  The height of the board remains the same throughout the pack, but the width of the board increases by 1 every 30 levels.  E.g, the board sizes for Fives are: 5x5x2, 5x6x2, 5x7x2, 5x8x2, 5x9x2.  As the board size increases, so does the average number of portals so that the density of the portals remains relatively constant within each pack.  Note that these 5 level packs cover all of the 25 board sizes used in the game.  

The Beginning/Double Trouble/Tripping Out/Crazy Quads

For these packs the board sizes increase in both height and width – but usually only one at a time.  The exception is Double Trouble – which features square boards from 5x5x2 to 9x9x2. 

Since the portals remain constant within each pack the portal density decreases significantly from the start to the end of each pack.  

Space/Time

The final two packs have the same board sizes – starting at 8x10x2 and finishing at 9x13x2 (the largest board in the game, also seen at the end of Nines).  In Space the portal averages remain constant for each group at 2.5 – portal density starts at 32 tiles and decreases to 46.8 at the end of the pack.  In Time, the average portals increases slightly every 30 levels – but not enough to keep pace with the size of the board. 

Pack Difficulty

The difficulty of each pack depends mostly on the number of portals and to a lesser extent the size of the board (again, read The Crazy Portal).  

Why aren’t they ordered based on difficulty?  Well they are – if you consider Fives through Nines from the portal based packs.  

I wanted the first 3 packs to show the craziness of the portal – this is harder to notice if the portals vary from level to level as they do in Fives through Nines.  

The board sizes in these packs also make it feel like a smooth progression in terms of difficulty: 

The Beginning starts at 5x5x2 (50 tiles) and finishes at 7x7x2 (98 tiles). 

Double Trouble starts at 5x5x2 (50 tiles) and finishes at 9x9x2 (162 tiles).  

Tripping Out starts at 5x8x2 (80 tiles) and finishes at 8x10x2 (160 tiles).  

From the end of The Beginning to the start of Double Trouble the board size is about halved – likewise with the end of Double Trouble to the start of Tripping Out.  The board size decrease roughly offsets the portal increase in terms of difficulty – but the vast increase in portal density makes the levels seem very different. 

I could have continued this progression and made Crazy Quads the next pack – but my feeling was that this pack is too hard to be at this stage.  Fives through Nines don’t feature the “smooth” progression of the first 3 packs – instead the start of each pack picks up at roughly the middle of the previous pack in terms of difficulty. 

When the progression first shifts – between Tripping Out and Fives – there is a huge drop in difficulty along with it – reaching about the same difficulty at Sevens. 

The shift back is much less clear: 

Nines have the largest board sizes in the game – but one of the lowest portal densities in the game.  The board size drops by over 30% going to Crazy Quads, but the number of portals increases, giving it the highest portal density of the game. 

The transition is even more apparent as the end of Nines and the beginning of Crazy Quads are both extremes within the extremes:  The board size drops from 234 to 108 tiles, while the average portals stays almost the same (4.27 to 4).  

My experience is that Nines takes a bit longer to complete than Crazy Quads – but I also score a higher percentage.  The end of Nines is harder than any set of 30 levels in Crazy Quads, though. 

Time was originally the sequel to Crazy Quads and averages 5 portals per level – though only a bit over half of the level have exactly 5 portals, with the rest split between 4 and 6 portals. 

The Space Pack

The Space pack is the newest level pack in CTD: Portals.  The board sizes are the same as the Time pack – which was renamed from Insanity to emphasize the difference between the 2 packs.  Only the Nines pack has a larger average board size – by 2.4 tiles.  The board sizes were chosen mainly to maximize use of the screen compared to Nines – where the earlier level groups are much taller than wide resulting in lots of wasted space on most devices. 

50% of the levels in Space have 2 portals, and the other 50% have 3 portals.  The average of 2.5 portals is less than the average of 2.86 portals in the game, despite the board sizes averaging 45% more tiles than the game average.  

This makes the portal density the lowest in the game at 39.12 tiles per portal.  

The dot density is also lowest in Space – the average of 10.66 tiles per dot is 25% higher than the next highest pack (Time, at 8.54 tiles/dot).  

Combining the two – on average there are 8.38 tiles for every portal/dot, with over 88% of the tiles being empty “space” – hence the name of the pack. 

The levels for space were aggressively filtered to minimize the number of dots – for the rest of the game, the filtering was determined by a formula (read more at Generating Levels).   With “normal” filtering – the average pairs of dots would have been about 2 higher than it is (9.17 pairs on average).

Dark Space

The levels in space were flipped as needed such that the bottom half – or dark side – always has equal or fewer dots than the top half.  Additionally – an adjustment was made to the filter criteria to give a bonus to levels with fewer dots on one half of the board.  

The result is that there are fewer than 7.3 dots on average on the dark side of the board 13.4 tiles per dot and 10.5 tiles per dot/portal.  Over 90% of the dark half is empty space – made more spacey by the darkness and lack of grid lines.  

Space and Time

Space is a stark contrast to the preceding pack (Crazy Quads) and the following pack (Time) – with a portal density less than half of either.  

It is meant to be a bit of a break – the “eye of the storm.”  There are no levels with fewer than 4 portals in Crazy Quads or Time – playing these packs back to back requires a lot of patience. 

The aggressive filtering makes the levels a bit more similar to each other than most packs – though there is still enough variety to keep it interesting and challenging. 

It took me multiple days to finish Time – and I only solved 31/150 puzzles without using hint mode.  I’m at nearly 70% perfect in Space through most of the pack.  It’s also taking a minute less on average to solve the puzzles – 75 seconds versus 135 seconds.  

 

Next page:  Evolution of Portals