Question 174
a) Show that it is not possible to separate the numbers of the set $A=\{1,2,3, \ldots, 10\}$ into two sets in which the product of the numbers in each of them is the same.
b) What is the smallest number of elements we need to remove from the set $A$ so that the remaining elements can be divided into two sets whose products of elements are equal? Show which numbers must be removed and how to separate the two sets.
b) What is the smallest number of elements we need to remove from the set $A$ so that the remaining elements can be divided into two sets whose products of elements are equal? Show which numbers must be removed and how to separate the two sets.