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25x25 puzzle factor tables
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Posted on: Thu Dec 02, 2021 6:33 am

Posts: 121
Joined: Tue Apr 24, 2012 7:47 pm
25x25 puzzle factor tables
Hello, everyone. Seventeen people have solved the 25x25 as of this message, and I'm sure Patrick and fzpowerman would love to see that number go even higher. To that end, I present you all with 2-cell and 3-cell factor tables. I made factoring tables for myself when I did the 19x19 and 20x20 puzzles, and the stuff I included was "made to order" specifically for them. The list below now covers 1-25 inclusive and may come in handy for solving fzpowerman's 25x25 behemoth. I don't know what exactly you're up against in Patrick's latest puzzle book, but this will hopefully be helpful. Although my lists do not and cannot possibly cover everything, I feel I've covered a decent amount. Enjoy!

skeeter84

2 cells

2 >>> 1x2
3 >>> 1x3
4 >>> 1x4; 2x2
5 >>> 5x1
6 >>> 1x6; 2x3
7 >>> 1x7
8 >>> 1x8; 2x4
9 >>> 1x9; 3x3
10 >>> 1x10; 2x5
11 >>> 1x11
12 >>> 1x12; 2x6; 3x4
13 >>> 1x13
14 >>> 1x14; 2x7
15 >>> 1x15; 3x5
16 >>> 1x16; 2x8; 4x4
17 >>> 1x17
18 >>> 1x18; 2x9; 3x6
19 >>> 1x19
20 >>> 1x20; 2x10; 4x5
21 >>> 1x21; 3x7
22 >>> 1x22; 2x11
23 >>> 1x23
24 >>> 1x24; 2x12; 3x8; 4x6
25 >>> 1x25; 5x5
26 >>> 2x13
27 >>> 3x9
28 >>> 2x14; 4x7
30 >>> 2x15; 3x10; 5x6
32 >>> 2x16; 4x8
34 >>> 2x17
35 >>> 5x7
36 >>> 2x18; 3x12; 4x9; 6x6
38 >>> 2x19
39 >>> 3x13
40 >>> 2x20; 4x10; 5x8
42 >>> 2x21; 3x14; 6x7
44 >>> 2x22; 4x11
45 >>> 3x15; 5x9
46 >>> 2x23
48 >>> 3x16; 4x12; 6x8; 2x24
49 >>> 7x7
50 >>> 2x25; 5x10
51 >>> 3x17
52 >>> 4x13
54 >>> 3x18; 6x9
55 >>> 5x11
56 >>> 4x14; 7x8
57 >>> 3x19
60 >>> 3x20; 4x15; 5x12; 6x10
63 >>> 3x21; 7x9
64 >>> 4x16; 8x8
65 >>> 5x13
66 >>> 3x22; 6x11
68 >>> 4x17
69 >>> 3x23
70 >>> 5x14; 7x10
72 >>> 8x9; 4x18; 6x12; 3x24
75 >>> 5x15; 3x25
76 >>> 4x19
77 >>> 7x11
78 >>> 6x13
80 >>> 4x20; 5x16; 8x10
84 >>> 6x14; 7x12; 4x21
85 >>> 5x17
88 >>> 4x22; 8x11
90 >>> 5x18; 6x15; 9x10
91 >>> 7x13
92 >>> 4x23
95 >>> 5x19
96 >>> 6x16; 8x12; 4x24
98 >>> 7x14
99 >>> 9x11
100 >>> 10x10; 5x20; 4x25
102 >>> 6x17
104 >>> 8x13
105 >>> 7x15; 5x21
108 >>> 6x18; 9x12
110 >>> 10x11; 5x22
112 >>> 7x16; 8x14
114 >>> 6x19
117 >>> 9x13
119 >>> 7x17
120 >>> 5x24; 6x20; 8x15; 10x12
126 >>> 7x18; 9x14; 6x21
128 >>> 8x16
130 >>> 10x13
133 >>> 7x19
135 >>> 9x15
136 >>> 8x17
140 >>> 7x20; 10x14
143 >>> 11x13
144 >>> 12x12; 9x16; 8x18; 6x24
147 >>> 7x21
150 >>> 10x15; 6x25
152 >>> 8x19
153 >>> 9x17
154 >>> 11x14; 7x22
162 >>> 9x18
168 >>> 7x24; 8x21; 12x14
170 >>> 10x17
171 >>> 9x19
175 >>> 7x25
176 >>> 11x16; 8x22
180 >>> 9x20; 10x18; 12x15
182 >>> 13x14
187 >>> 11x17
190 >>> 10x19
192 >>> 8x24; 12x16
198 >>> 9x22; 11x18
200 >>> 8x25; 10x20
204 >>> 12x17
208 >>> 13x16
209 >>> 11x19
210 >>> 10x21; 14x15
216 >>> 9x24; 12x18
220 >>> 10x22; 11x20
221 >>> 13x17
224 >>> 14x16
225 >>> 9x25; 15x15
234 >>> 13x18
238 >>> 14x17
240 >>> 12x20; 15x16; 10x24
252 >>> 12x21; 14x18
255 >>> 15x17
260 >>> 13x20
266 >>> 14x19
270 >>> 15x18
272 >>> 16x17
280 >>> 14x20
285 >>> 15x19
288 >>> 12x24; 16x18
294 >>> 14x21
304 >>> 16x19
306 >>> 17x18
315 >>> 15x21
322 >>> 14x23
323 >>> 17x19
325 >>> 13x25
336 >>> 14x24; 16x21
340 >>> 17x20
342 >>> 18x19
360 >>> 18x20; 15x24
384 >>> 16x24
408 >>> 17x24
420 >>> 20x21

3 cells

90 >>> 2x5x9; 2x15x3; 3x5x6; 3x10x3; 9x10x1; 15x1x6; 18x1x5
210 >>> 1x10x21; 1x14x15; 2x7x15; 2x5x21; 3x5x14; 3x7x10; 5x6x7
216 >>> 18x2x6; 18x3x4; 18x12x1; 12x6x3; 12x2x9; 6x6x6; 6x4x9; 3x8x9; 24x3x3; 24x1x9
280 >>> 20x14x1; 20x7x2; 14x10x2; 10x7x4; 14x5x4; 8x7x5
378 >>> 21x1x18; 21x2x9; 21x3x6; 6x7x9; 14x3x9; 18x3x7
539 >>> 11x7x7
540 >>> 12x5x9; 12x15x3; 15x6x6; 15x4x9; 10x9x6; 18x15x2; 20x9x3; 18x10x3; 18x5x6
594 >>> 3x9x22; 3x11x18; 6x9x11
650 >>> 2x13x25; 5x10x13
672 >>> 2x14x24; 2x16x21; 3x14x16; 4x7x24; 4x8x21; 4x12x14; 6x7x16; 6x8x14; 7x8x12
715 >>> 5x11x13

720 >>> 2x18x20; 2x15x24; 3x12x20; 3x15x16; 3x10x24; 4x9x20; 4x10x18; 4x12x15; 5x12x12; 5x9x16; 5x8x18; 5x6x24; 6x6x20; 6x8x15; 6x10x12; 8x9x10

756 >>> 21x2x18; 21x3x12; 21x4x9; 21x6x6; 18x14x3; 18x7x6; 14x9x6; 12x9x7
850 >>> 25x2x17; 5x10x17
935 >>> 5x11x17
1026 >>> 19x18x3; 19x9x6
1040 >>> 4x13x20; 5x13x16; 8x10x13
1080 >>> 3x18x20; 3x15x24; 4x15x18; 5x9x24; 5x12x18; 6x9x20; 6x10x18; 6x12x15; 8x9x15; 9x10x12
1254 >>> 22x3x19; 19x11x6
1280 >>> 20x8x8; 20x16x4; 16x10x8; 16x16x5
1326 >>> 6x13x17
1360 >>> 4x17x20; 5x16x17; 8x10x17
1547 >>> 17x13x7
1989 >>> 9x13x17
1995 >>> 21x5x19; 19x15x7
2380 >>> 10x14x17; 20x17x7
2448 >>> 24x6x17; 12x12x17; 8x17x18; 17x16x9
2754 >>> 18x17x9
4080 >>> 10x17x24; 12x17x20; 15x16x17
4845 >>> 15x17x19

Last edited by skeeter84 on Fri Dec 03, 2021 3:33 am, edited 1 time in total.

Posted on: Thu Dec 02, 2021 11:31 am

Posts: 838
Joined: Fri May 13, 2011 6:51 pm
Re: 25x25 puzzle factor tables
skeeter84 wrote:
Hello, everyone. Seventeen people have solved the 25x25 as of this message, and I'm sure Patrick and fzpowerman would love to see that number go even higher. To that end, I present you all with 2-cell and 3-cell factor tables. I made factoring tables for myself when I did the 19x19 and 20x20 puzzles, and the stuff I included was "made to order" specifically for them. The list below now covers 1-25 inclusive and may come in handy for solving fzpowerman's 25x25 behemoth. I don't know what exactly you're up against in Patrick's latest puzzle book, but this will hopefully be helpful. Although my lists do not and cannot possibly cover everything, I feel I've covered a decent amount. Enjoy!

skeeter84

2 cells ...

Thank you for the tables , good compilation job.
It will be useful. A comment. Two cells must be contiguous so combinations of the type 2x2, 3x3, 4x4, 5x5, 6x6, 7x7, 8x8, ... are never possible, that is, the table can be simplified a little bit (same for 6x6x6 for 216... ).

In the other hand, I observe the lack of other combinations like 100 in two cells (4x25; 5x20), 48 in 3 cells, etc., but it is clear that it's not possible to give all possible factorizations (the number of combinations, only without repetition, of 25 numbers, taken in groups of 3, is 2,300, so the list would be terrible.

Posted on: Thu Dec 02, 2021 11:50 pm

Posts: 121
Joined: Tue Apr 24, 2012 7:47 pm
Re: 25x25 puzzle factor tables
Hi, clm - I'm glad you liked my tables. I'm well aware that a 2-cell cage cannot contain the same number. I listed combos with repeat digits in case I come across a scenario like the one below:

90x in 3 cells and this cage contains a 10. The remaining product is 90/10 = 9. There are 2 ways to get the product of 9: 1x9 and 3x3. If this cage were in a straight line, 10x3x3 would be impossible since 3 repeats within a row or column. If, on the other hand, the cage in question were L-shaped, 10x3x3 COULD be the correct answer. I made no distinction between L-shaped and straight line cages for my 3-cell combos, and my list covers both shapes simultaneously. Once again, I made my original combo tables for the 19x19 and 20x20 puzzles. In a 9x9 or 10x10 puzzle, 8x9 is the only way to get a product of 72 with 2 digits. In a 12x12, though, the answer might be 12x6 instead. When solving puzzles of different sizes, I simply exclude any combos with numbers above the puzzle's maximum digit. I probably should include more combos into my tables whenever I have time, though.

skeeter84

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