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Skip to 4th power (Posted on 2016-06-27) Difficulty: 3 of 5
1
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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

No Solution Yet Submitted by Jer    
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Some Thoughts convincing but not a proof | Comment 1 of 4
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


  Posted by Charlie on 2016-06-27 19:57:01
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