I have the answer to an algebra equation that is the solution to a card
trick, but I do not understand the theory that allows the final step of the
solution to be valid.
Someone selects two cards and given the cards are '5' and '3,' the
following equation can be reached:
'10x + y = 53'
Dividing 53 by 10, the quotient is 5 and the remainder is 3, but I do not
understand what theory would make this step valid. I have considered simple
division and mod-ing, but I still don't understand what theory or property
makes this possible.
With the equation:
'12x + y = 38,'
dividing 38 by 12, the quotient is 3 and the remainder is 2, which are the
values of the two cards selected in another manipulation of the same card
trick. I believe this has something to do with varying the base of the
equation, but I'm still unsure of what makes this valid or if it is even
correct.
Thank you for any help.
trick, but I do not understand the theory that allows the final step of the
solution to be valid.
Someone selects two cards and given the cards are '5' and '3,' the
following equation can be reached:
'10x + y = 53'
Dividing 53 by 10, the quotient is 5 and the remainder is 3, but I do not
understand what theory would make this step valid. I have considered simple
division and mod-ing, but I still don't understand what theory or property
makes this possible.
With the equation:
'12x + y = 38,'
dividing 38 by 12, the quotient is 3 and the remainder is 2, which are the
values of the two cards selected in another manipulation of the same card
trick. I believe this has something to do with varying the base of the
equation, but I'm still unsure of what makes this valid or if it is even
correct.
Thank you for any help.