# Tag Archives: reasoning

## Twin Liars

Kerry and Kelly are twins. One of them lies on Mondays, Tuesdays, and Wednesdays and tells the truth on the other days of the week. The other lies on Thursdays, Fridays, and Saturdays and tells the truth on the other … Continue reading

## Mean of Numbers

The mean of a set of numbers is . If one number is increased by , the mean increases to . How many numbers are in the set? Source: NCTM Mathematics Teacher, January 2006 Solution The formula for the mean … 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

## Colored Balls

A bowl contains colored balls: green, red, blue, yellow, black, and white. If you are blindfolded, what is the smallest number of balls you must pick to guarantee that you have at least balls of the same color? Source: NCTM … Continue reading

## Filling a Square

The square shown here can be filled in so that each row and each column contains each of the numbers , and exactly once. What does equal? Source: NCTM Mathematics Teacher 2006 SOLUTION Fill in the fourth column: goes in … Continue reading

## Postal Worker

A postal worker has houses on his route. During one snowy day, he noticed that every other house’s mailbox was blocked by snow, and he could not deliver the mail. He also noticed that he had no mail to deliver … Continue reading

## Building Blocks (Level 1)

You have an unlimited supply of cubes. Each cube’s side length is a number of the form , where is any nonnegative integer. That is, there are cubes with edges of length unit, units, units, units, units, and so on. … Continue reading

## Digit Exchange

A three-digit number increases by nine if you exchange the second and third digits. The same three-digit number increases by if you exchange the first and second digits. By how much will the number increase if you exchange the first … Continue reading