(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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