Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1987 based on Ordered pair.

Ordered pair Problem – AIME I, 1987


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.

  • is 107
  • is 300
  • is 840
  • cannot be determined from the given information

Key Concepts


Integers

Ordered pair

Algebra

Check the Answer


But try the problem first…

Answer: is 300.

Source
Suggested Reading

AIME I, 1987, Question 1

Elementary Algebra by Hall and Knight

Try with Hints


First hint

for no carrying required

Second Hint

the range of possible values of any digit m is from 0 to 1492 where the value of n is fixed

Final Step

Number of ordered pair (1+1)(4+1)(9+1)(2+1)

=(2)(5)(10)(3)

=300.

Subscribe to Cheenta at Youtube