Young Axl Rose and Cake Cream in 2022! :D

[MHF]

I'm going to summon Abby with some math curios:

12 x 42 = 21 x 24
12 x 63 = 21 x 36
12 x 84 = 21 x 48
13 x 62 = 31 x 26
13 x 93 = 31 x 39
14 x 82 = 41 x 28
21 x 24 = 12 x 42
21 x 36 = 12 x 63
21 x 48 = 12 x 84
23 x 64 = 32 x 46
23 x 96 = 32 x 69
24 x 63 = 42 x 36
24 x 84 = 42 x 48
26 x 31 = 62 x 13
26 x 93 = 62 x 39
28 x 41 = 82 x 14
31 x 39 = 13 x 93
32 x 46 = 23 x 64
32 x 69 = 23 x 96
34 x 86 = 43 x 68
36 x 42 = 63 x 24
36 x 84 = 63 x 48
39 x 62 = 93 x 26
42 x 48 = 24 x 84
43 x 68 = 34 x 86
46 x 96 = 64 x 69
48 x 63 = 84 x 36
64 x 69 = 46 x 96

The division side of the numerals from before.

144648 = (861 X 168) = (492 X 294) = {[(41 + 43) - 2] X 42^2} = {(41 + 43 - 2) X 42 X [(-3 + 5) X (-1 + 7^2 - 3^3)]} ---> 41_43__24_42__351_173.

185472 = (672 X 276) = (384 X 483) = {[(-3^3 + 7^2 + 1) X (10 + 5 - 3)] X (2 X 42) X (1 + 4 + 3)} ---> 371_153__24_42__41_43.

And,

9949716 = (3852 X 2583) = (1476 X 6741) = ((41 + 43 - 2) X 42 X {[0^2 + (-001)^03 + 5^02 + 3^2^0] X [+7^3^0 + (-10)^02 + 0]}) ---> 41_43__24_42__153_371.

16746912 = (6552 X 2556) = (4473 X 3744) = ({-(0^0^3) X -(010^2^0) X (-7) - (3 X 3) + (5^02) X (010^3) X (0^0)} X (2 X 42) X (1 + 4 + 3)) ---> 173_351__24_42__41_43.



Almost 4:17

For example, 124 x 842 = 248 x 421 and 1224 x 8442 = 2448 x 4221

Written, say, firstly, as 124 / 421 = 248 / 842 .

This prompt appears in Boris Kordemsky's The Moscow Puzzles (1956), in which Kordemsky lists the full set of equations of this type.

The Moscow Puzzles: 359 Mathematical Recreations Paperback – April 10 1992
by Boris A. Kordemsky (Author)