Other tags that relate to 2-digit Square
Difference of two squares. Factors and multiples. Divisibility. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Place value. Addition & subtraction. Expanding and factorising quadratics. Generalising. Integers.There are 128 results
Broad Topics > Thinking Mathematically > Generalising
Plus Minus
Age 14 to 16
Challenge Level
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Mini-max
Age 11 to 14
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. . . .
Repeaters
Age 11 to 14
Challenge Level
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
What's Possible?
Age 14 to 16
Challenge Level
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Chocolate Maths
Age 11 to 14
Challenge Level
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Special Sums and Products
Age 11 to 14
Challenge Level
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
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.
One O Five
Age 11 to 14
Challenge Level
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Have You Got It?
Age 11 to 14
Challenge Level
Can you explain the strategy for winning this game with any target?
Number Pyramids
Age 11 to 14
Challenge Level
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Three Times Seven
Age 11 to 14
Challenge Level
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Adding in Rows
Age 11 to 14
Challenge Level
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
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?
What Numbers Can We Make Now?
Age 11 to 14
Challenge Level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Got it for Two
Age 7 to 14
Challenge Level
Got It game for an adult and child. How can you play so that you know you will always win?
Counting Factors
Age 11 to 14
Challenge Level
Is there an efficient way to work out how many factors a large number has?
Multiplication Square
Age 14 to 16
Challenge Level
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Mind Reading
Age 11 to 14
Challenge Level
Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .
Summing Consecutive Numbers
Age 11 to 14
Challenge Level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Regular Hexagon Loops
Age 11 to 14
Challenge Level
Make some loops out of regular hexagons. What rules can you discover?
Hypotenuse Lattice Points
Age 14 to 16
Challenge Level
The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
Take Three from Five
Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
One, Three, Five, Seven
Age 11 to 16
Challenge Level
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
Sums of Pairs
Age 11 to 16
Challenge Level
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Games Related to Nim
Age 5 to 16
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Nim
Age 14 to 16
Challenge Level
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Got It
Age 7 to 14
Challenge Level
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Winning Lines
Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Lower Bound
Age 14 to 16
Challenge Level
What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =
Sum Equals Product
Age 11 to 14
Challenge Level
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so. . . .
Chocolate 2010
Age 14 to 16
Challenge Level
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
Neighbourly Addition
Age 7 to 14
Challenge Level
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Consecutive Negative Numbers
Age 11 to 14
Challenge Level
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Nim-7
Age 5 to 14
Challenge Level
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Nim-7 for Two
Age 5 to 14
Challenge Level
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Steps to the Podium
Age 7 to 14
Challenge Level
It starts quite simple but great opportunities for number discoveries and patterns!
Magic Letters
Age 11 to 14
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?
Mindreader
Age 11 to 14
Challenge Level
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Beelines
Age 14 to 16
Challenge Level
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
What Numbers Can We Make?
Age 11 to 14
Challenge Level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Great Granddad
Age 11 to 14
Challenge Level
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Janine's Conjecture
Age 14 to 16
Challenge Level
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
How Much Can We Spend?
Age 11 to 14
Challenge Level
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Window Frames
Age 5 to 14
Challenge Level
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Pentanim
Age 7 to 16
Challenge Level
A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
Harmonic Triangle
Age 14 to 16
Challenge Level
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Maths Trails
Age 7 to 14
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
NRICH is part of the family of activities in the Millennium Mathematics Project.