Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2012 based on Arrangement of digits.
Let B be the set of all binary integers that can be written using exactly 5 zeros and 8 ones where leading zeros are allowed. If all possible subtractions are performed in which one element of B is subtracted from another, find the number of times the answer 1 is obtained.
Arrangements
Algebra
Number Theory
Answer: is 330.
AIME, 2012, Question 5
Combinatorics by Brualdi
When 1 subtracts from a number, the number of digits remain constant when the initial number has units and tens place in 10
Then for subtraction from B requires one number with unit and tens place 10.
10 there, remaining 1 distribute any of other 11 then answer \({11 \choose 7} = {330}\).
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.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.