# Tag Archives: counting

## Bowling Pins

After rolling the first ball of a frame in a game of 10-pin bowling, how many different pin configurations can remain (assuming all configurations are physically possible)? Source: NCTM Mathematics Teacher, September 2006 Solution A pin configuration is made up … Continue reading

## Divisible by 7

How many four digit positive integers divisible by have the property that, when the first and last digits are interchanged, the result is a (not necessarily four-digit) positive integer divisible by ? Source: NCTM Mathematics Teacher, October 2006 Solution Is … Continue reading

## Waiting in Line

In a movie theater line, people are behind Mark, who is places in front of Sam. If there are people in front of Sam, how many people are in line? Source: NCTM Mathematics Teacher, October 2006 Solution The figure illustrates … Continue reading

## Largest of Five Integers

A set contains five integers. When distinct elements of this set are added together, two at a time, the complete list of different possible sums is , and . What is the largest of the five integers in the set? … Continue reading

## Same Difference

If fifteen distinct whole numbers are randomly selected from to inclusive, determine the probability that two pairs of these numbers will have the same difference. Source:NCTM Mathematic Teacher, January 2006 Solution What are the possible difference values? There are possible … Continue reading

## Pip Total as Prime Number

A pair of six-sided dice is tossed. What is the probability that the pip total is a prime number? Source: NCTM Mathematics Teacher, January 2006 Solution Number of possible outcomes Desirable outcomes Number of desirable outcomes Probability that the pip … Continue reading

## Numbers Greater Than 5,000,000

Using all the digits and , how many distinct integers greater than can be formed? Source: NCTM Mathematics Teacher, January 2006 Solution The first digit must be a or a . Case 1: _ _ _ _ _ _ Since … Continue reading

## Ten Different Digits

What is the probability that a number chosen at random from the range to inclusive will contain ten different digits? Round your answer to the nearest millionth. Source: NCTM Mathematics Teacher, January 2006 Solution We divide the large range into … Continue reading

## Changing Seats

Thirty-five students are seated in five rows and seven columns. Is it possible for the students to change seats if every student must move exactly one seat to the left, right, front or back? Source: NCTM Mathematics Teacher, January 2006 … Continue reading

## Sum of Consecutive Numbers (Part 2)

The sum of consecutive positive integers is . Find all possible values of . Source: NCTM Mathematics Teacher, December 2005 SOLUTION Let be the sum of consecutive positive integers with the first term equal . If we add the first … Continue reading