As I played the first few levels, I noticed something interesting. The first four level passwords were as follows:
Level Password
01 00512
02 01536
03 01024
04 03072
Two of the passwords being powers of two immediately caught my attention. If we convert each password to binary (using sixteen bits just because bits usually come in groups of eight), we get this:
Level Password Binary
01 00512 0000001000000000
02 01536 0000011000000000
03 01024 0000010000000000
04 03072 0000110000000000
Following this pattern, I expected the password for level
05
to be 0000100000000000
, or 02048
, but using this password brought me to level 07
instead. Going back to level 04
, I played up to level 08
and found that, while there was still clearly some kind of pattern, it was a bit more complicated than I had thought. Converting the first eight level passwords to binary, we have:
Level Password Binary
01 00512 0000001000000000
02 01536 0000011000000000
03 01024 0000010000000000
04 03072 0000110000000000
05 03584 0000111000000000
06 02560 0000101000000000
07 02048 0000100000000000
08 06144 0001100000000000
At this point, we can already start to see what's going on, if we look at the binary in columns. There seems to be a pattern emerging:
- The 29 bit column (10th from the right) has 2 ones, 2 zeros, 2 ones, and 2 zeros; we might expect this to continue indefinitely.
- The 210 bit column (11th from the right), after a single zero, has 4 ones in a row, followed by some zeros; we might expect this column to have a pattern of 4 ones, 4 zeros, and so on, albeit offset by a single zero at the beginning.
However, I didn't really see it until I had played through another eight levels. Converting the first sixteen level passwords to binary, we have:
Level Password Binary
01 00512 0000001000000000
02 01536 0000011000000000
03 01024 0000010000000000
04 03072 0000110000000000
05 03584 0000111000000000
06 02560 0000101000000000
07 02048 0000100000000000
08 06144 0001100000000000
09 06656 0001101000000000
10 07680 0001111000000000
11 07168 0001110000000000
12 05122 0001010000000010
13 05634 0001011000000010
14 04610 0001001000000010
15 04098 0001000000000010
16 12290 0011000000000010
Focusing only on the higher-order (leftmost) bits, we can now clearly see that:
- The 29 bit, starting at level
01
, has a pattern of 2 ones, 2 zeros, and so on. - The 210 bit, starting at level
02
, seems to have a pattern of 4 ones, 4 zeros, and so on. - The 211 bit, starting at level
04
, has 8 ones in a row, and has presumably started a pattern of 8 ones, 8 zeros, and so on. - The 212 bit, starting at level
08
, is all ones all the way through level16
, and may have started a pattern of 16 ones, 16 zeros, and so on. - The 213 bit first becomes one at level
16
.
But something is also happening in the 21 bit (second from the right), where a one suddenly appears starting at level
12
. This doesn't seem related to the rest of the pattern, and I think I know why.It was after completing level
11
that the little ant protagonist found... a bag of Quavers...? (Did I mention that
Pushover was sponsored by a snack food company? I've never had Quavers;
apparently they're British.) On the menu screen which appears between levels, I could see after completing level 11
that a little sprite representing a bag of Quavers had been added to
the bottom of the screen where there appear to be nine spaces
available. So it's probably safe to assume that nine virtual bags of Quavers are pointlessly
awarded throughout the game.The fact that the 21 bit changed after level
11
suggests that some of the lower-order bits are used for tracking the bags collected, independently of the higher-order bits which indicate the level number. As an experiment, I took the password for level 12
and flipped the 21 bit to zero, resulting in 0001010000000000
or 05120
. Sure enough, entering the password 05120
took me to level 12
, and upon completing the level, the inter-level menu screen did not show the bag that was there when I had beaten levels 11
through 15
before. Moreover, the password it gave me for level 13
this time was 05632
, which is the previously obtained level 13
password with the 21 bit flipped to zero. However, taking the level 02
password and flipping the 21 bit to one did not result in a valid password. So I cannot cheat my way into already having a bag prior to level 12
, but it seems I can enter levels 12
or later without one.If some bits are only for tracking bags collected, and if any level can be entered without any bags, then we should be able to get a complete set of level passwords just by predicting the pattern of the bits indicating level number. The passwords of levels
01
through 16
suggested that only the higher-order bits (starting with 29) encoded the level number. So at this point, I predicted that the full pattern (if it continued indefinitely) would be as follows:- The 29 bit will start with one at level
01
and then change every 2 levels. - The 210 bit will become one at level
02
and then change every 4 levels. - The 211 bit will become one at level
04
and then change every 8 levels. - The 212 bit will become one at level
08
and then change every 16 levels. - The 213 bit will become one at level
16
and then change every 32 levels. - The 214 bit will become one at level
32
and then change every 64 levels. - The 215 bit will become one at level
64
and then change every 128 levels.
This algorithm does predicts the values of the seven highest-order bits for the first sixteen level passwords. Unfortunately, I realized later that it's not quite correct. While looking around in the game's files for goodies, I found that the Steam version of Pushover comes with a file called
PUSHCODE.TXT
— which, bizarrely, contains most but not all level passwords, and seems to have been written not by the developer or publisher but by someone from a demogroup known as Tristar & Red Sector Incorporated. The file begins:
TRISTAR & RED SECTOR
PRESENTS
PUSHOVER (LEVELCODES)
LEVEL 1 00512
LEVEL 2 01536
LEVEL 3 01024
...
It continues all the way through level
67
:
...
LEVEL 65 17023
LEVEL 66 18047
LEVEL 67 17535
NOTE: THERE ARE MISSING A FEW CODES!!!!
TIME BANDIT/TRSI
Pushover apparently has 100 levels, so I guess the player who wrote this file gave up about two-thirds of the way through the game. However, they got far enough to show me that the 215 bit does not get flipped to one at level 64. Any number with a one in the 215 place would be at least 32768, and none of the passwords in
PUSHCODE.TXT
are that high!So I wrote a few lines of Python to convert all the passwords in
PUSHCODE.TXT
to binary. The results are as follows:
Level Password Binary
01 00512 0000001000000000
02 01536 0000011000000000
03 01024 0000010000000000
04 03072 0000110000000000
05 03584 0000111000000000
06 02560 0000101000000000
07 02048 0000100000000000
08 06144 0001100000000000
09 06656 0001101000000000
10 07680 0001111000000000
11 07168 0001110000000000
12 05122 0001010000000010
13 05634 0001011000000010
14 04610 0001001000000010
15 04098 0001000000000010
16 12290 0011000000000010
17 12802 0011001000000010
18 13826 0011011000000010
19 13314 0011010000000010
20 15362 0011110000000010
21 15878 0011111000000110
22 14854 0011101000000110
23 14342 0011100000000110
24 10246 0010100000000110
25 10758 0010101000000110
26 11782 0010111000000110
27 11270 0010110000000110
28 09222 0010010000000110
29 09734 0010011000000110
30 08718 0010001000001110
31 08206 0010000000001110
32 24590 0110000000001110
33 25102 0110001000001110
34 26126 0110011000001110
35 25614 0110010000001110
36 27662 0110110000001110
37 28174 0110111000001110
38 27150 0110101000001110
39 26638 0110100000001110
40 30734 0111100000001110
41 31246 0111101000001110
42 32270 0111111000001110
43 31758 0111110000001110
44 29726 0111010000011110
45 30238 0111011000011110
46 29214 0111001000011110
47 28702 0111000000011110
48 20510 0101000000011110
49 21022 0101001000011110
50 22046 0101011000011110
51 21534 0101010000011110
52 23582 0101110000011110
53 24094 0101111000011110
54 23070 0101101000011110
55 22558 0101100000011110
56 18494 0100100000111110
57 19006 0100101000111110
58 20030 0100111000111110
59 19518 0100110000111110
60 17470 0100010000111110
61 17982 0100011000111110
62 16958 0100001000111110
63 16510 0100000001111110
64 16511 0100000001111111
65 17023 0100001001111111
66 18047 0100011001111111
67 17535 0100010001111111
This is all consistent with my predictions about bits 29 through 214, but it's the 20 bit — not the 215 bit — which gets flipped to one at level
64
. So we can revise the earlier prediction:- The 29 bit starts with one at level
01
and then changes every 2 levels. - The 210 bit becomes one at level
02
and then changes every 4 levels. - The 211 bit becomes one at level
04
and then changes every 8 levels. - The 212 bit becomes one at level
08
and then changes every 16 levels. - The 213 bit becomes one at level
16
and then changes every 32 levels. - The 214 bit becomes one at level
32
and then changes every 64 levels. - The 20 bit becomes one at level
64
and then changes every 128 levels.
This isn't quite as elegant as what I had initially predicted, because the "level bits" are no longer contiguous, but it appears to be correct. The last rule is already unlike the others anyway, in that we would never actually see the 20 bit change from one back to zero after 128 levels because there are only 100 levels in the game. I predicted that bit to flip at a frequency of once per 128 levels to continue the power-of-two pattern. So that last rule could just be written as:
- The 20 bit is one at level
64
and up.
The passwords in
PUSHCODE.TXT
also give us a hint about how bags are tracked. It seems that each one has its own dedicated bit. If we enter the level 67
password above (17535
or 0100010001111111
) and then quit back to the menu screen, we see that we have the first six bags. But if we flip a few bits to get 0100010001010101
, and enter the corresponding decimal password 17493
, quitting back to the menu shows that we have only the second, fourth, and sixth bags.If there are nine bags, and if each bag has its own bit, then we need nine bits to represent them all. Meanwhile, if bits 20 and 29 through 214 and are used to determine the level, then the nine bits remaining to represent bags are 21 through 28 and 215.
From another source (the description on this YouTube video), I've found that level
100
is actually a bonus level, and that its password is 44543
(or, in binary, 1010110111111111
). This is is still consistent with the above rules regarding bits 29, 210, 211, 212, 213, 214, and 20; additionally, bits 21, 22, 23, 24, 25, 26, 27, 28, and 215 are all flipped to one.By starting with the level
100
password, individually setting the 21, 22, 23, 24, 25, 26, 27, 28, and 215 bits back to zero, entering the resulting passwords to start level 100,
and then quitting to the menu to see which bags are shown, I've confirmed that each of these bits corresponds to a particular bag. Interestingly, setting 215 to zero in particular, resulting in the password 11775
, has the effect of making level 100
easier by revealing the special domino types which are normally hidden on this bonus level. More importantly, though, I'm pretty sure we have now fully decoded the game's level passwords.- The 20 bit is one at level
64
and up. - The 21 bit is one after the first bag is collected (level ≥
12
). - The 22 bit is one after the second bag is collected (level ≥
21
). - The 23 bit is one after the third bag is collected (level ≥
30
). - The 24 bit is one after the fourth bag is collected (level ≥
44
). - The 25 bit is one after the fifth bag is collected (level ≥
56
). - The 26 bit is one after the sixth bag is collected (level ≥
63
). - The 27 bit is one after the seventh bag is collected (level ≥
78
). - The 28 bit is one after the eighth bag is collected (level ≥
89
). - The 29 bit starts with one at level
01
and then changes every 2 levels. - The 210 bit becomes one at level
02
and then changes every 4 levels. - The 211 bit becomes one at level
04
and then changes every 8 levels. - The 212 bit becomes one at level
08
and then changes every 16 levels. - The 213 bit becomes one at level
16
and then changes every 32 levels. - The 214 bit becomes one at level
32
and then changes every 64 levels. - The 215 bit is one after the ninth bag is collected (level =
100
).
The above assumes that bags are awarded for completion of levels
11
, 20
, 29
, 43
, 55
, 62
, 77
, and 88
, based on the binary representations of the first 67 passwords passwords found in PUSHCODE.TXT
and of the remaining passwords found on this page. I don't feel inclined to play through the entire game to confirm it myself before publishing this post. Given that we can enter any level just by setting the "level bits" (29, 210, 211, 212, 213, 214, and 20) — without turning on any of the "bag bits" — there's actually more than enough information here to allow me to amuse myself by writing a little Python script that gives me a valid password for any level I want to play:
import sys
def get_level_bit(frequency, level):
offset = frequency // 2
return (level + offset) // frequency % 2
def generate_password(level):
bits = 0
for index in reversed(range(16)):
bits = bits << 1
if 9 <= index <= 14:
bits += get_level_bit(2 ** (index - 8), level)
if index == 0:
bits += get_level_bit(128, level)
return bits
if __name__ == "__main__":
print(generate_password(int(sys.argv[1])))
Is this really useful when I could just look up the passwords on the internet? Not really. But reverse engineering the game's passwords was more fun.