Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Ordered pair.
An ordered pair (m,n) of non-negative integers is called simple if the additive m+n in base 10 requires no carrying. Find the number of simple ordered pairs of non-negative integers that sum to 1492.
Integers
Ordered pair
Algebra
Answer: is 300.
AIME I, 1987, Question 1
Elementary Algebra by Hall and Knight
for no carrying required
the range of possible values of any digit m is from 0 to 1492 where the value of n is fixed
Number of ordered pair (1+1)(4+1)(9+1)(2+1)
=(2)(5)(10)(3)
=300.
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