Question 28
One night, Wanderson dreamed of two three-digit numbers: $$
a b c \text{ and } d e f,
$$ so that the sum $$
a b c + d e f + a b c d e f
$$ coincided with the sum of all three-digit numbers. Note that $a b c$ is not the product of the digits $a, b$ and $c$, but the three digit number $a, b$ and $c$. The same goes for the other numbers.
a) Calculate the sum of all three-digit numbers.
b) Show that Wanderson's dream is an impossible dream.
a b c \text{ and } d e f,
$$ so that the sum $$
a b c + d e f + a b c d e f
$$ coincided with the sum of all three-digit numbers. Note that $a b c$ is not the product of the digits $a, b$ and $c$, but the three digit number $a, b$ and $c$. The same goes for the other numbers.
a) Calculate the sum of all three-digit numbers.
b) Show that Wanderson's dream is an impossible dream.