**(for Primary Students or above)**

The following table
shows the square of a sequence of consecutive numbers. You can
find that there is an interesting recurring pattern of the last
digit of the product, i.e. **0,1,4,9,6,5,6,9,4,1**.

Do you know why? Think about it and I am sure that you can find out the answer easily.

0 |
X |
0 |
= |
0 |

1 |
X |
1 |
= |
1 |

2 |
X |
2 |
= |
4 |

3 |
X |
3 |
= |
9 |

4 |
X |
4 |
= |
16 |

5 |
X |
5 |
= |
25 |

6 |
X |
6 |
= |
36 |

7 |
X |
7 |
= |
49 |

8 |
X |
8 |
= |
64 |

9 |
X |
9 |
= |
81 |

10 |
X |
10 |
= |
100 |

11 |
X |
11 |
= |
121 |

12 |
X |
12 |
= |
144 |

13 |
X |
13 |
= |
169 |

14 |
X |
14 |
= |
196 |

15 |
X |
15 |
= |
225 |

16 |
X |
16 |
= |
256 |

17 |
X |
17 |
= |
289 |

18 |
X |
18 |
= |
324 |

19 |
X |
19 |
= |
361 |

20 |
X |
20 |
= |
400 |

21 |
X |
21 |
= |
441 |

22 |
X |
22 |
= |
484 |

23 |
X |
23 |
= |
529 |

24 |
X |
24 |
= |
576 |

25 |
X |
25 |
= |
625 |

26 |
X |
26 |
= |
676 |

27 |
X |
27 |
= |
729 |

28 |
X |
28 |
= |
784 |

29 |
X |
29 |
= |
841 |

30 |
X |
30 |
= |
900 |

31 |
X |
31 |
= |
961 |

32 |
X |
32 |
= |
1024 |

33 |
X |
33 |
= |
1089 |

34 |
X |
34 |
= |
1156 |

35 |
X |
35 |
= |
1225 |

36 |
X |
36 |
= |
1296 |

37 |
X |
37 |
= |
1369 |

38 |
X |
38 |
= |
1444 |

39 |
X |
39 |
= |
1521 |

40 |
X |
40 |
= |
1600 |

41 |
X |
41 |
= |
1681 |

42 |
X |
42 |
= |
1764 |

43 |
X |
43 |
= |
1849 |

44 |
X |
44 |
= |
1936 |

45 |
X |
45 |
= |
2025 |

46 |
X |
46 |
= |
2116 |

47 |
X |
47 |
= |
2209 |

48 |
X |
48 |
= |
2304 |

49 |
X |
49 |
= |
2401 |

50 |
X |
50 |
= |
2500 |

51 |
X |
51 |
= |
2601 |

52 |
X |
52 |
= |
2704 |

53 |
X |
53 |
= |
2809 |

54 |
X |
54 |
= |
2916 |

55 |
X |
55 |
= |
3025 |

56 |
X |
56 |
= |
3136 |

57 |
X |
57 |
= |
3249 |

58 |
X |
58 |
= |
3364 |

59 |
X |
59 |
= |
3481 |

23 JANUARY, 1999

Please click to see the comment and relationship with magic square.

What has been will be again, what has been done will be done again; there is nothing new under the sun.--Ecclesiastes 1:9

[Recurring Pattern] [Relation with the Magic Square] [Create a Magic Square by Excel]

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