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# Multiples Grid

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Age 7 to 11

Challenge Level

*Multiples Grid printable sheet*

Here is a 100 grid with some numbers shaded:

1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |

11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |

21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |

31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |

41 |
42 |
43 |
44 |
45 |
46 |
47 |
48 |
49 |
50 |

51 |
52 |
53 |
54 |
55 |
56 |
57 |
58 |
59 |
60 |

61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
69 |
70 |

71 |
72 |
73 |
74 |
75 |
76 |
77 |
78 |
79 |
80 |

81 |
82 |
83 |
84 |
85 |
86 |
87 |
88 |
89 |
90 |

91 |
92 |
93 |
94 |
95 |
96 |
97 |
98 |
99 |
100 |

What do all the numbers shaded blue have in common?

What do you notice about all the numbers shaded pink?

Can you work out why two of the numbers are shaded in a purple colour?

Now, here is part of a 100 square shaded in a different way:

24 |
25 |
26 |

34 |
35 |
36 |

44 |
45 |
46 |

Can you explain the shading this time?

Here are some more parts of the 100 square, each one shaded according to different rules. Can you work out what the rules are for each?

Is there only one solution each time?

66 |
67 |
68 |

76 |
77 |
78 |

86 |
87 |
88 |

34 |
35 |
36 |

44 |
45 |
46 |

54 |
55 |
56 |

5 |
6 |
7 |

15 |
16 |
17 |

25 |
26 |
27 |

*This problem is featured in Maths Trails: Excel at Problem Solving, one of the books in the Maths Trails series written by members of the NRICH Team and published by Cambridge University Press.*

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?