# Monthly Archives: June 2014

## Juneau Average Temperature

If the average daily temperature in Juneau, Alaska, during the first days of January was , what must the daily average be during the remainder of the month if Juneau’s January average is to match the historical average of ? … Continue reading

## Sum of Squares

The eighteenth-century mathematician Joseph Louis Lagrange proved that every positive integer is the sum of, at most, four squares. Find at least one way to write as the sum of three squares. Source: NCTM Mathematics Teacher 2008 SOLUTION a sum … Continue reading

## Average of Two Numbers

The average of and is . The average of and equals the average of and . Find the value of . Source: NCTM Mathematics Teacher 2008 SOLUTION Average of and Average of and Simplify Eq. Substitute the value of from … Continue reading

## Age of Siblings

Frances, a middle school student, observed that her age cubed was greater than her little brother’s age raised to the 7th power by exactly the difference in their ages. How old are the siblings? Source: NCTM Mathematics Teacher 2008 SOLUTION … Continue reading

## Six-sided Die

A 6-sided die is labeled with the first prime numbers instead of the first integers to . The die is rolled twice. What is the probability that the sum of the rolls is a prime number? Source: NCTM Mathematics Teacher … Continue reading

## ISBN

Commercially published books bear a 10-digit identification number called an ISBN. Let denote the digits from left to right. Each ISBN has the property that is divisible by . Given the correct ISBN , how many possible pairs of digits … Continue reading