Proper Patterns

Given some of the proper factors of a number, what could the number be?

Squaring Legs

Using information about how a scroboscopus squares its number of legs, can you tell how many scroboscopi Tom bought?

The Middle Digit

Investigate the pattern(s) involving the middle digit in the square of numbers whose digits are all 1’s.

Breaking the Code

Use what you know or what you can find out about common letters to help you decode this message.

Counting Terms

How many terms are in the given sequence?

Average Patterns

Use the average of four 26’s and four 34’s to determine the average of four of another number.

Sprinting Around

When will Sonic the Hedgehog, the Road Runner, and the Tasmanian Devil meet if they are running on a circular track following the patterns described?

Missing Letters

Find the next two letters in the given sequence.

Number Machine

What will the number machine give me if I put in 100?

Even Factors

Find numbers whose factors are all even (excluding the number 1 as a factor).

Not So Good Partitions

Find all positive whole numbers that are not “good” numbers.

Laying Bricks

How many ways are there to lay bricks to form different patio patterns?

Row Sum

In the given arrangement of numbers, investigate the sum of all the numbers in a row.

Alpha Numeric

Fill in the next letter of the alphabet, using the logic established to list the first eight.

Triangular Array

What numeral will be listed directly beneath 125 when the triangular array is continued?

What is the value of the expression?

Counting Stones

Following the counting pattern described, which of the original nine stones is counted as stone #599?

How many times will the digits of each number in a set add to equal 8?

It is important for 8000 people to hear a rumor by May 14. Is this outcome likely to occur if the pattern for spreading the rumor continues as started?

Units of Seven

Find the units digit of a large number.

Theater Seating

How many seats are in the Mathematics Theater?

Playing for Sticks

Devise a strategy so that you will always win the game.

Horizontal Inquisition

Draw the next figure in the sequence. Explain how you determined the result.

Foil Frenzy

Simplify an expression.

What Time is It?

Determine the next value in the sequence.

The Next Row

Complete the row using a pattern.

Tessellating a Plane

Determine why some polygons tessellate the plane and why others do not.

Fractal Iterations

Explore the idea of fractals.

Repeating Patterns

Find the pattern to count numbers.

Sum of Natural Numbers

Find a way to add a set of natural numbers.

Triangles inside Triangles

Extend the given table and determine a relationship between the numbers in the triangle.

Triangular Numbers

Form triangular numbers and look for patterns.

Sum of Consecutive Integers

Use the sum of consecutive integers to form certain numbers.

Completing the Sequence

Find the next numbers in the sequences.

Squares on a Checkerboard

Determine how may squares are on a given checkerboard.