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minus-squarenandeEbisu@lemmy.mllinkfedilinkarrow-up30·edit-22 years agoHuh, that’s true of any number that ends in 9. XY + X + Y = 10*X + Y Y’s cancel, XY = 9X => Y = 9 for any non-zero finite value of X. so for 69? X = 6, Y=9 (6*9) + 6 + 9 = 10*6 + 9 54 + 15 = 69 69 = 69 (nice!) 429? X = 42 Y = 9 (42*9) + 42 + 9 =10*42 + 9 (378) + 51 = 429 429 = 429 Even if 10X+Y doesn’t equal something that ends in 9 it works X=3.14 Y=9 (3.14*9) + 3.14 + 9 = 10*3.14 + 9 28.26 + 12.14 = 40.4 40.4 = 40.4 Doesn’t work if Y =\= 9: 68? X = 6 Y = 8 (6*8) + 6 + 8 ?= 10*6 + 8 (48) + 14 ?= 68 62 =\= 68
minus-squareevilgiraffe666@ttrpg.networklinkfedilinkarrow-up1·2 years agoI wanted to try to properly prove that it didn’t work for y!=9, but I think you covered the edge cases - X=0 or unbounded. Well done!
Huh, that’s true of any number that ends in 9.
XY + X + Y = 10*X + Y
Y’s cancel,
XY = 9X => Y = 9 for any non-zero finite value of X.
so for 69? X = 6, Y=9
(6*9) + 6 + 9 = 10*6 + 9
54 + 15 = 69
69 = 69 (nice!)
429? X = 42 Y = 9
(42*9) + 42 + 9 =10*42 + 9
(378) + 51 = 429
429 = 429
Even if 10X+Y doesn’t equal something that ends in 9 it works
X=3.14 Y=9
(3.14*9) + 3.14 + 9 = 10*3.14 + 9
28.26 + 12.14 = 40.4
40.4 = 40.4
Doesn’t work if Y =\= 9:
68? X = 6 Y = 8
(6*8) + 6 + 8 ?= 10*6 + 8
(48) + 14 ?= 68
62 =\= 68
I wanted to try to properly prove that it didn’t work for y!=9, but I think you covered the edge cases - X=0 or unbounded. Well done!