by Joanna Hung

some research on MATHEMATICS

(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


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