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Resources tagged with Properties of numbers similar to Be Reasonable:

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Broad Topics > Numbers and the Number System > Properties of numbers

A Little Light Thinking

Age 14 to 16 Challenge Level:

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

An Introduction to Irrational Numbers

Age 14 to 18

Tim Rowland introduces irrational numbers

Triangular Triples

Age 14 to 16 Challenge Level:

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

What Are Numbers?

Age 7 to 18

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.

Generating Triples

Age 14 to 16 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

A Long Time at the Till

Age 14 to 18 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

Pair Products

Age 14 to 16 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Few and Far Between?

Age 14 to 18 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

Robert's Spreadsheet

Age 14 to 16 Challenge Level:

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Babylon Numbers

Age 11 to 18 Challenge Level:

Can you make a hypothesis to explain these ancient numbers?

Rachel's Problem

Age 14 to 16 Challenge Level:

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

Odd Differences

Age 14 to 16 Challenge Level:

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Really Mr. Bond

Age 14 to 16 Challenge Level:

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

Enriching Experience

Age 14 to 16 Challenge Level:

Find the five distinct digits N, R, I, C and H in the following nomogram

Fracmax

Age 14 to 16 Challenge Level:

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

Times Right

Age 11 to 16 Challenge Level:

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Factorial

Age 14 to 16 Challenge Level:

How many zeros are there at the end of the number which is the product of first hundred positive integers?

Difference Dynamics

Age 14 to 18 Challenge Level:

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Prime Magic

Age 7 to 16 Challenge Level:

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Filling the Gaps

Age 14 to 16 Challenge Level:

Which numbers can we write as a sum of square numbers?