• nandeEbisu@lemmy.ml
    37·
    1 year ago

    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

    • evilgiraffe666@ttrpg.network
      4·
      1 year ago

      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!

      • nandeEbisu@lemmy.ml
        2·
        1 year ago

        I’m an engineering major, we learn all of the edge cases as “well technically this isn’t always true, but we’ll just pretend it is because the results are close enough”