# Monthly Archives: January 2013

## Odd Squares

On an checkerboard, how many different squares can be made using an odd number of squares? Source: mathcontest.olemiss.edu 11/6/2006 SOLUTION This problem is similar to the problem titled “Chess Anyone” dated 2/8/2010. A smaller checkerboard How many squares in a … Continue reading

## Spotâ€™s Doghouse

Spot’s doghouse has a regular hexagonal base that measures one yard on each side. Spot is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside the doghouse that Spot can … Continue reading

## Cubical Dice

A cube is formed by gluing together standard cubical dice. (On a standard die, the sum of the numbers of any pair of opposite faces is .) Find the smallest possible sum of all the numbers showing on the surface … Continue reading

## Two-Digit Prime Numbers

The digits , and are used to form four two-digit prime numbers, with each digit used exactly once. What is the sum of these four primes? Source: NCTM Mathematics Teacher SOLUTION The digits , and cannot be the units digit … Continue reading

## Parallelogram in Isosceles Triangle

The length of the base of an isosceles triangle is a quarter of its perimeter. From an arbitrary point on the base straight lines are drawn parallel to the sides of the triangle. How many times is the perimeter of … Continue reading

## Same Arc Length

If an arc of on circle has the same length as an arc of on circle , find the ratio of the area of circle to the area of circle . Source: NCTM Mathematics Teacher SOLUTION Let be the radius … Continue reading

## Seven Tangent Circles

Each of the small circles in the figure has radius 1. The innermost circle is tangent to the six circles that surround it, and each of those circles is tangent to the large circle and to its small-circle neighbors. Find … Continue reading

## Area in Right Triangle

In the diagram, is a right angle. Point is on , and bisects . Points and are on and , respectively, so that and . Given that and , find the integer closest to the area of quadrilateral . Source: … Continue reading

## Product of Powers

Find the sum of all positive integers , where and are non-negative integers, for which is not a divisor of . Source: NCTM Mathematics Teacher SOLUTION For ease in notation, let and For not to divide we want or . … Continue reading

## Surface Area of Cube

Three of the vertices of a cube are and . What is the surface area of the cube? Source: NCTM Mathematics Teacher SOLUTION Distance formula in 3-dimension of a segment defined by two end points and Apply the formula to … Continue reading