2016 AMC 8 Problem 24 Number Theory

2016 AMC 8 Problem 24 Number Theory

 Understand the Problem The digits , , , , and  are each used once to write a five-digit number . The three-digit number  is divisible by , the three-digit number  is divisible by , and the three-digit number  is divisible by . What is ? Source of the problem 2016 AMC...
2017 AMC 8 Problem 21 Number Theory

2017 AMC 8 Problem 21 Number Theory

Understand the problem Suppose , , and  are nonzero real numbers, and . What are the possible value(s) for           ? Source of the problem 2017 AMC 8 Problem 21 Topic Number Theory Difficulty Level Easy Suggested Book Excursion in Mathematics Start with hints Hint...
2018 AMC 10A Problem 25 Number Theory

2018 AMC 10A Problem 25 Number Theory

Understand the problem For a positive integer  and nonzero digits , , and , let  be the -digit integer each of whose digits is equal to ; let  be the -digit integer each of whose digits is equal to , and let  be the -digit (not -digit) integer each of whose digits is...
AMC 2019 12A Problem 15 Diophantine Equation

AMC 2019 12A Problem 15 Diophantine Equation

Understand the problem Positive real numbers  and  have the property thatand all four terms on the left are positive integers, where log denotes the base 10 logarithm. What is ? Source of the problem 2019 AMC 12A Problems/Problem 15 Topic logarithm, diophantine...
2008 AMC 8 Problem 22 Number theory

2008 AMC 8 Problem 22 Number theory

                                    Understand the Problem For how many positive integer values of (n) are both ( frac {n}{3} ) and ( 3n ) three-digit whole numbers? Source of the problem 2008 AMC 8 Problem 22 Topic Number Theory Difficulty Level Easy Suggested Book...
Does there exist a Magic Rectangle?

Does there exist a Magic Rectangle?

Magic Squares are infamous; so famous that even the number of letters on its Wikipedia Page is more than that of Mathematics itself. People hardly talk about Magic Rectangles. Ya, Magic Rectangles! Have you heard of it? No, right? Not me either! So, I set off to...