# Math Contest Problems

- Author:
- Kevin Hopkins

- Topic:
- Mathematics

What follows is my attempt at creating worksheets that produce problems like math contest problems. This is not easy to do as most math contests pride themselves on offering original problems to challenge students, so it is difficult to find "families" of problems that can be algorithmically generated.
In most problems you see Answer followed by a ? . Replace the ? with the answer you come up with. On hitting enter, the page should grade your submitted answer.
Most ideas for these pages originated with MATHCOUNTS minis videos at http://www.artofproblemsolving.com/Videos/index.php?type=minis, MAA Curriculum Inspiration video based off AMC competitions at http://www.maa.org/math-competitions/teachers/curriculum-inspirations, Art of Problem Solving videos at http://www.artofproblemsolving.com/Videos/index.php, Art of Problem Solving Books at http://www.artofproblemsolving.com/Store/curriculum.php or Dr. Hopkins' work with hosting competitions written by http://mathleague.org. Art of Problem Solving also has a free resource known as Alcumus, http://www.artofproblemsolving.com/liz/Alcumus/index.php, which teaches some of this material and presents problems about it.
Many math contests exist. You can find many of them at https://sites.google.com/site/sbumathcon/home/other-math-contests.
Dr. Hopkins has been interested in contests for years, even running a camp called Math Contest Camp. 2018 will be the 13th year of this camp. You can find information about 2018 at https://sites.google.com/site/sbumathcon/math-contest-camp-2018. Check the camp website for more information.
If you have other suggestions for families of problems to include, please email those to Dr. Hopkins, khopkins@sbuniv.edu . If there is a source of the problem, or a source of an explanation for the problem, please send me that as well so I can include it with the worksheet. Also, please report any errors. If you think you have entered a correct answer and the worksheet says it is incorrect, please take a screenshot of this and email it to me. There may be a special case in the worksheet that I failed to account for and so the worksheet doesn't operate in that special case.
It is also possible that I just did the problem wrong and only thought I was correct. This was certainly unintentional. In math, no one chooses to do a problem wrong. We may do it wrong because we misread the problem, made a careless error, are trying to mislead someone (which I am not) or some other reason. In life that is not always the case. We unfortunately make poor decisions to do something wrong knowing full well we are doing something wrong (and ignoring the possible consequences of that action). God knew this was possible and I believe He has provided a way for us to deal with that problem. For my explanation of that solution, you can view a Facebook video of a presentation of that: https://www.facebook.com/photo.php?v=569730479736877&set=vb.417886931587900&type=3&theater (you do have to be logged into Facebook to view this video).

## Table of Contents

### Elementary Type Contests

- Estimating Sums
- Estimating Products
- Estimating Products Part 2
- Estimating Quotients
- Estimating Square Roots
- Estimating Squares of Numbers
- Estimation Golf with Timer
- Solve Simple Equations
- Finding middle Number
- Counting Elements in a List
- Counting Multiples
- Probability of Selecting a Multiple from a List
- How Many Outcomes?
- Counting with Venn Diagrams
- Spinner Probability
- More Spinner Probability
- Signed Subtraction
- Extended Subtraction
- Visual Patterns

### Middle School Type Contests

- Unit Digit of Powers
- Using Ratios
- Pythagorean Theorem
- Curve Stitching
- Converting to Another Base
- Other Number Bases
- Recognizing squares
- Function Rule-Section 1.3
- Function Table-Section 1.3
- Function Graphs-Section 1.3
- New Operations
- Probability
- Probability and Multiplication
- Probability with Lengths
- Summing a List
- How Many Divisors
- How many EVEN (or ODD) Divisors does a number have?
- Sum of all divisors of a number
- Greatest Common Divisor
- Least Common Multiple
- Simplify Factorials
- Find the Largest Prime Factor of expression with factorials
- Handshake Problem
- From 2015 National Countdown Round
- Counting Paths

### High School Type Contests

- Checkerboard Relay Problem
- Hexagonal Numbers as Relay Question
- Recursive Function as Relay Question
- Counting Handshakes as a Relay Question
- Sum of List Relay
- Base Relay
- Angle Sum Relay
- Triangular Numbers Relay
- Counting Committees as Relay Question
- Counting More Complicated Committees
- Harmonic Mean Relay
- Factors Relay
- More on Counting Committees
- Counting Marbles
- Probability with Area
- Area Between Concentric Circles

### Useful Geometry Theorems

### Useful Theorems, not Geometry