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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.

## Other useful links

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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