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
etc...
Show that adding all the numbers that are not crossed off from 1 to the end of a line, the result is a 4th power.
Example: 1+4+5+6=16=24
The first hundred such totals and their exact 4th roots:
1 1
16 2
81 3
256 4
625 5
1296 6
2401 7
4096 8
6561 9
10000 10
14641 11
20736 12
28561 13
38416 14
50625 15
65536 16
83521 17
104976 18
130321 19
160000 20
194481 21
234256 22
279841 23
331776 24
390625 25
456976 26
531441 27
614656 28
707281 29
810000 30
923521 31
1048576 32
1185921 33
1336336 34
1500625 35
1679616 36
1874161 37
2085136 38
2313441 39
2560000 40
2825761 41
3111696 42
3418801 43
3748096 44
4100625 45
4477456 46
4879681 47
5308416 48
5764801 49
6250000 50
6765201 51
7311616 52
7890481 53
8503056 54
9150625 55
9834496 56
10556001 57
11316496 58
12117361 59
12960000 60
13845841 61
14776336 62
15752961 63
16777216 64
17850625 65
18974736 66
20151121 67
21381376 68
22667121 69
24010000 70
25411681 71
26873856 72
28398241 73
29986576 74
31640625 75
33362176 76
35153041 77
37015056 78
38950081 79
40960000 80
43046721 81
45212176 82
47458321 83
49787136 84
52200625 85
54700816 86
57289761 87
59969536 88
62742241 89
65610000 90
68574961 91
71639296 92
74805201 93
78074896 94
81450625 95
84934656 96
88529281 97
92236816 98
96059601 99
100000000 100
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
For grpSize = 1 To 200
For i = 1 To grpSize
DoEvents
term = term + 1
If grpSize Mod 2 = 1 Then tot = tot + term
Next
If grpSize Mod 2 = 1 Then
Text1.Text = Text1.Text & tot & " "
rt = Sqr(Sqr(tot))
Text1.Text = Text1.Text & rt & crlf
End If
Next
Text1.Text = Text1.Text & crlf & " done"
End Sub
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Posted by Charlie
on 2016-06-27 19:57:01 |
convincing but not a proof
