Resources tagged with Properties of numbers similar to Investigating Pascal's Triangle:
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Investigations. Mathematical reasoning & proof. Patterned numbers. Properties of numbers. Arithmetic sequence. Generalising. Digital roots. Maths Supporting SET. Geometric sequence. Working systematically.There are 65 results
Broad Topics > Numbers and the Number System > Properties of numbers
Four Coloured Lights
Stage: 3 Challenge Level: 
Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
Can You Find a Perfect Number?
Stage: 2 and 3
Can you find any perfect numbers? Read this article to find out more...
Numbers Numbers Everywhere!
Stage: 1 and 2
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Helen's Conjecture
Stage: 3 Challenge Level:
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Three Neighbours
Stage: 2 Challenge Level:
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
One to Eight
Stage: 3 Challenge Level:
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
Small Change
Stage: 3 Challenge Level:
In how many ways can a pound (value 100 pence) be changed into some combination of 1, 2, 5, 10, 20 and 50 pence coins?
Like Powers
Stage: 3 Challenge Level:
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
Cogs
Stage: 3 Challenge Level:
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Happy Octopus
Stage: 3 Challenge Level:
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.
Escape from the Castle
Stage: 2 Challenge Level:
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Whole Numbers Only
Stage: 3 Challenge Level:
Can you work out how many of each kind of pencil this student bought?
Chameleons
Stage: 3 Challenge Level:
Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .
Always, Sometimes or Never? Number
Stage: 2 Challenge Level:
Are these statements always true, sometimes true or never true?
Even So
Stage: 3 Challenge Level:
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Lesser Digits
Stage: 3 Challenge Level:
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
The Patent Solution
Stage: 3 Challenge Level:
A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?
Slippy Numbers
Stage: 3 Challenge Level:
The number 10112359550561797752808988764044943820224719 is called a 'slippy number' because, when the last digit 9 is moved to the front, the new number produced is the slippy number multiplied by 9.
Summing Consecutive Numbers
Stage: 3 Challenge Level:
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Counting Factors
Stage: 3 Challenge Level:
Is there an efficient way to work out how many factors a large number has?
Babylon Numbers
Stage: 3, 4 and 5 Challenge Level:
Can you make a hypothesis to explain these ancient numbers?
Elevenses
Stage: 3 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
28 and It's Upward and Onward
Stage: 2 Challenge Level:
Can you find ways of joining cubes together so that 28 faces are visible?
Water Lilies
Stage: 3 Challenge Level:
There are some water lilies in a lake. The area that they cover doubles in size every day. After 17 days the whole lake is covered. How long did it take them to cover half the lake?
Thirty Six Exactly
Stage: 3 Challenge Level:
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Got it Article
Stage: 2 and 3
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Six Times Five
Stage: 3 Challenge Level:
How many six digit numbers are there which DO NOT contain a 5?
See the Light
Stage: 2 and 3 Challenge Level:
Work out how to light up the single light. What's the rule?
X Marks the Spot
Stage: 3 Challenge Level:
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
The Codabar Check
Stage: 3
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.
Mini-max
Stage: 3 Challenge Level:
Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .
Unit Fractions
Stage: 3 Challenge Level:
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
Triangular Triples
Stage: 3 Challenge Level:
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Special Numbers
Stage: 3 Challenge Level:
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Take One Example
Stage: 1 and 2
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Unlocking the Case
Stage: 2 Challenge Level:
A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?
Arrange the Digits
Stage: 3 Challenge Level:
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
Oh! Hidden Inside?
Stage: 3 Challenge Level:
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Magic Letters
Stage: 3 Challenge Level:
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Please Explain
Stage: 3 Challenge Level:
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
Table Patterns Go Wild!
Stage: 2 Challenge Level:
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
Guess the Dominoes
Stage: 1, 2 and 3 Challenge Level:
This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.
Snail One Hundred
Stage: 1 and 2 Challenge Level:
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Which Numbers? (1)
Stage: 2 Challenge Level:
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
Which Numbers? (2)
Stage: 2 Challenge Level:
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Guess the Dominoes for Two
Stage: Early years, 1 and 2 Challenge Level:
Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.
Cinema Problem
Stage: 3 Challenge Level:
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
NRICH is part of the family of activities in the Millennium Mathematics Project.