text: # Search by Topic
  
  #### Resources tagged with Visualising similar to Differs:
  
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  ### Triangles Within Triangles
  
  ##### Stage: 4 Challenge Level:
  
  Can you find a rule which connects consecutive triangular numbers?
  
  ### Natural Sum
  
  ##### Stage: 4 Challenge Level:
  
  The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
  
  ### Triangles Within Squares
  
  ##### Stage: 4 Challenge Level:
  
  Can you find a rule which relates triangular numbers to square numbers?
  
  ### Three Frogs
  
  ##### Stage: 4 Challenge Level:
  
  Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .
  
  ### Triangles Within Pentagons
  
  ##### Stage: 4 Challenge Level:
  
  Show that all pentagonal numbers are one third of a triangular number.
  
  ### Mystic Rose
  
  ##### Stage: 4 Challenge Level:
  
  Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
  
  ### Coordinate Patterns
  
  ##### Stage: 3 Challenge Level:
  
  Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
  
  ### More Pebbles
  
  ##### Stage: 2 and 3 Challenge Level:
  
  Have a go at this 3D extension to the Pebbles problem.
  
  ### Changing Places
  
  ##### Stage: 4 Challenge Level:
  
  Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
  
  ### The Triangle Game
  
  ##### Stage: 3 and 4 Challenge Level:
  
  Can you discover whether this is a fair game?
  
  ### Seven Squares - Group-worthy Task
  
  ##### Stage: 3 Challenge Level:
  
  Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
  
  ### Jam
  
  ##### Stage: 4 Challenge Level:
  
  To avoid losing think of another very well known game where the patterns of play are similar.
  
  ### Yih or Luk Tsut K'i or Three Men's Morris
  
  ##### Stage: 3, 4 and 5 Challenge Level:
  
  Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
  
  ### Jam
  
  ##### Stage: 4 Challenge Level:
  
  A game for 2 players
  
  ### Sliding Puzzle
  
  ##### Stage: 1, 2, 3 and 4 Challenge Level:
  
  The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
  
  ### AMGM
  
  ##### Stage: 4 Challenge Level:
  
  Can you use the diagram to prove the AM-GM inequality?
  
  ### Hypotenuse Lattice Points
  
  ##### Stage: 4 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?
  
  ### Picture Story
  
  ##### Stage: 4 Challenge Level:
  
  Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
  
  ### Building Gnomons
  
  ##### Stage: 4 Challenge Level:
  
  Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
  
  ### Rotating Triangle
  
  ##### Stage: 3 and 4 Challenge Level:
  
  What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
  
  ### Intersecting Circles
  
  ##### Stage: 3 Challenge Level:
  
  Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?
  
  ### Seven Squares
  
  ##### Stage: 3 Challenge Level:
  
  Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
  
  ### Steel Cables
  
  ##### Stage: 4 Challenge Level:
  
  Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
  
  ### Proximity
  
  ##### Stage: 4 Challenge Level:
  
  We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
  
  ### Dice, Routes and Pathways
  
  ##### Stage: 1, 2 and 3
  
  This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .
  
  ### Problem Solving, Using and Applying and Functional Mathematics
  
  ##### Stage: 1, 2, 3, 4 and 5 Challenge Level:
  
  Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
  
  ### There and Back Again
  
  ##### Stage: 3 Challenge Level:
  
  Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
  
  ### Konigsberg Plus
  
  ##### Stage: 3 Challenge Level:
  
  Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
  
  ### Playground Snapshot
  
  ##### Stage: 2 and 3 Challenge Level:
  
  The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
  
  ##### Stage: 3 Challenge Level:
  
  Can you mark 4 points on a flat surface so that there are only two different distances between them?
  
  ### Flight of the Flibbins
  
  ##### Stage: 3 Challenge Level:
  
  Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .
  
  ### Squares, Squares and More Squares
  
  ##### Stage: 3 Challenge Level:
  
  Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
  
  ### Travelling Salesman
  
  ##### Stage: 3 Challenge Level:
  
  A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
  
  ### Tourism
  
  ##### Stage: 3 Challenge Level:
  
  If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
  
  ### On the Edge
  
  ##### Stage: 3 Challenge Level:
  
  If you move the tiles around, can you make squares with different coloured edges?
  
  ### Coloured Edges
  
  ##### Stage: 3 Challenge Level:
  
  The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
  
  ### You Owe Me Five Farthings, Say the Bells of St Martin's
  
  ##### Stage: 3 Challenge Level:
  
  Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
  
  ### Zooming in on the Squares
  
  ##### Stage: 2 and 3
  
  Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
  
  ### Cubes Within Cubes
  
  ##### Stage: 2 and 3 Challenge Level:
  
  We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
  
  ### Convex Polygons
  
  ##### Stage: 3 Challenge Level:
  
  Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
  
  ### Tilting Triangles
  
  ##### Stage: 4 Challenge Level:
  
  A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
  
  ### Diagonal Dodge
  
  ##### Stage: 2 and 3 Challenge Level:
  
  A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
  
  ### Pattern Power
  
  ##### Stage: 1, 2 and 3
  
  Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
  
  ### Painting Cubes
  
  ##### Stage: 3 Challenge Level:
  
  Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
  
  ### Cutting a Cube
  
  ##### Stage: 3 Challenge Level:
  
  A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
  
  ### Tetrahedra Tester
  
  ##### Stage: 3 Challenge Level:
  
  An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
  
  ##### Stage: 3 Challenge Level:
  
  Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
  
  ### Tied Up
  
  ##### Stage: 3 Challenge Level:
  
  In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
  
  ### Trice
  
  ##### Stage: 3 Challenge Level:
  
  ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
  
  ### Framed
  
  ##### Stage: 3 Challenge Level:
  
  Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
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