Euclid 2020/Problem 2
2.
(a) The three-digit positive integer 
is odd and has three distinct digits. If the
hundreds digit of m equals the product of the tens digit and ones (units) digit of
, what is ?
(b) Eleanor has 100 marbles, each of which is black or gold. The ratio of the number
of black marbles to the number of gold marbles is 
. How many gold marbles
should she add to change this ratio to 
?
(c) Suppose that n is a positive integer and that the value of
is an integer. Determine all possible values of 
.
