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## Extremal Principle for Counting – AMC 10

Extremal Principle is used in a variety of problems in Math Olympiad. The following problem from AMC 10 is a very nice example of this idea. AMC 10 Problem 4 (2019) A box contains 28 red balls, 20 green balls, 19 yellow balls, 13 blue balls, 11 white balls, and 9...

## AMC 10A Year 2014 Problem 20 Sequential Hints

Understand the problem The product $$(8)(88888……8)$$, where the second factor has k digits, is an integer whose digits have a sum of $$1000$$. What is k? Source of the problem American Mathematical Contest 10A Year 2014 Topic Number Theory  Difficulty...

## Combinatorics – AMC 10A 2008 Problem 23 Sequential Hints

Understand the problem Two subsets of the set  are to be chosen so that their union is  and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter? Source of the...

## AMC 10A Year 2005 Problem 21 Sequential Hints

Understand the problem For how many positive integers (n) does 1+2+3+4+….+n evenly divide from 6n? (a)3.       (b)5.       (c)7.       (d)9.       (e)11 Source of the problem American Mathematical Contest 2005 10A Problem 21 Topic Number Theory  Difficulty Level...

## AMC 10A Year 2005 Problem 22 Sequential Hints

Understand the problem Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. How many elements are common to S and T? (a) 166.       (b)333.      (c)500.      (d)668.      (e)1001 Source of...

## AMC 10A Year 2006 Problems 21 Sequential Hints

Understand the problem How many 4 digit positive numbers have at least that is a 2 or a 3? (a)2439.     (b)4096.     (c)4903.     (d)4904.     (e)5416 Source of the problem American Mathematical Contest 2006 10 A Problem 21 Topic Combinatorics  Difficulty Level 4/10...