## Set of Primes

Let be the set of primes that divide . What is the largest integer so that the set of primes that divides is equal to ? Source: NCTM Mathematics Teacher, August 2006 Solution The next prime greater than is . … Continue reading

## Father and Son Eat Together

A father and son eat meals together. If the son eats twice as fast as the father and the father eats a meal in minutes, how many meals can the son eat in hours? Source: NCTM Mathematics Teacher, August 2006 … Continue reading

## Round Table

A round table can be made square by dropping the four leaves. If a side of a square table measures inches, to the nearest hundredth of a square inch, how much smaller is the area of the table when the … Continue reading

## Children Sharing Money

Al, Bee, Cecil, and Di have , and , respectively. Their father proposed that Al and Bee share their wealth equally, and then Bee and Cecil do likewise, and then Cecil and Di. Their mother’s plan is the same except … Continue reading

## Cottages on a Straight Road

There are four cottages on a straight road. The distance between Ted’s and Alice’s cottages is km. Both Bob’s and Carol’s cottages are twice as far from Alice’s as they are from Ted’s. Find the distance between Bob’s and Carol’s … Continue reading

## Partners in Integers

Two integers are said to be partners if both are divisible by the same set of prime numbers. Find the number of positive integer less than that have no partners less than . Source: NCTM Mathematics Teacher, August 2006 Solution … Continue reading

## Water in Glass Box

A glass box cm, closed on all six sides, is partially filled with colored water. When the box is placed on one of its sides, the water level is cm above the table. If the box is placed on one … Continue reading

## Making Triangles

You have six sticks of lengths , and cm. Find the number of noncongruent triangles that can be formed using three of these sticks as sides. Source: NCTM Mathematics Teacher, August 2006 Solution Three sticks make a triangle. There are … Continue reading

## Product of x-Intercepts

The line with equation and with equation are perpendicular. If neither passes through the origin, find the product of their -intercepts. Source: SCVMA Math Olympiad 2010 Solution Let point represent the -intercept of line Let point represent the -intercept of … Continue reading

## Five Same Numbers

You roll five fair, six-sided dice, all at the same time. In that one roll, what is the probability of getting five of the same number? Source: NCTM Mathematics Teacher, September 2006 Solution When you roll five dice at the … Continue reading