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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 |

For accessibility, clicking on the 'show' button below a table in this activity will show a description of the table.

Pink numbers: 5, 10, 15, 20, 25, 30, 40, 45, 50, 55, 60, 65, 75, 80, 85, 90, 95, 100

Blue numbers: 7, 14, 21, 28, 42, 49, 56, 63, 77, 84, 91, 98

Purple numbers: 35, 70

Orange numbers: all others

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 |

Pink numbers: 24, 26, 34, 36, 44, 46

Blue number: 35

Orange numbers: 25, 45

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 |

Blue numbers: 66, 77

Purple number: 88

Orange numbers: 67, 68, 76, 78, 86, 87

34 |
35 |
36 |

44 |
45 |
46 |

54 |
55 |
56 |

Purple numbers: 36, 54

Blue number: 45

Orange numbers: 34, 35, 44, 46, 55, 56

5 |
6 |
7 |

15 |
16 |
17 |

25 |
26 |
27 |

Pink number: 16

Blue number: 27

Orange numbers: 5, 6, 7, 15, 17, 25, 26

*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.*