This is a beautiful problem from ISI MSTAT 2019 PSA problem 6 based on basic counting principles. We provide sequential hints so that you can try.
How many times does the digit ‘2’ appear in the set of integers \( \{1,2,…,1000\} \)?
Basic counting principles
Answer: is 300
ISI MStat 2019 PSA Problem 6
A First Course in Probability by Sheldon Ross
Let’s count the number of times 2 occurs once.
_ _ _
The position of 2 can be selected in 3 ways. The rest in 9 x 9.
Total number of 2 = 1 x 3 x 9 x 9 = 243
Let’s count the number of times 2 occurs twice.
_ _ _
The positions of 2 can be selected in 3 ways. The rest in 9.
Total number of 2 = 2 x 3 x 9 = 54
Let’s count the number of times 2 occurs thrice.
The positions of 2 can be selected in 1 way. The rest in 1.
Total number of 2 = 3 x 1 x 1 = 3
Total Number of Such Numbers = 243 + 54 + 3 = 300
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
