How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

Digits and Order | AIME I, 1992 | Question 2

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Digits and Order.

Digits and order - AIME I, 1992

A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. Find number of ascending positive integers are there.

  • is 107
  • is 502
  • is 840
  • cannot be determined from the given information

Key Concepts




Check the Answer

Answer: is 502.

AIME I, 1992, Question 2

Elementary Number Theory by David Burton

Try with Hints

First hint

There are nine digits that we use 1,2,3,4,5,6,7,8,9.

Second Hint

Here each digit may or may not be present.

\(\Rightarrow 2^{9}\)=512 potential ascending numbers, one for subset of {1,2,3,4,5,6,7,8,9}

Final Step

Subtracting empty set and single digit set



Subscribe to Cheenta at Youtube

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.