I have another 10cm x 13cm x 14cm block of cheese just like in
Cheese Cut Conclusion. Again I am slicing ten 1cm slices off of the block, all parallel to the faces like the original problem.
How many different sizes can the remaining block be after all ten slices are removed?
The output of the below program has been sorted and appears below it:
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
For a = 0 To 9
For b = 0 To 10
c = 10 - a - b
If c >= 0 Then
d1 = 10 - a
d2 = 13 - b
d3 = 14 - c
vol = d1 * d2 * d3
low = d1
If d2 < low Then low = d2
If d3 < low Then low = d3
high = d1
If d2 > high Then high = d2
If d3 > high Then high = d3
middle = 27 - low - high
Text1.Text = Text1.Text & mform(vol, "####0") & mform(low, "####0") & mform(middle, "####0") & mform(high, "####0") & " " & mform(d1, "####0") & mform(d2, "####0") & mform(d3, "####0") & crlf
End If
Next
Next
Text1.Text = Text1.Text & crlf & " done"
End Sub
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
sides
sides (remains of
volume in order 10 13 14)
168 1 12 14 1 12 14
169 1 13 13 1 13 13
308 2 11 14 2 11 14
312 2 12 13 2 12 13
312 2 12 13 2 13 12
420 3 10 14 3 10 14
420 3 10 14 10 3 14
429 3 11 13 3 11 13
429 3 11 13 3 13 11
432 3 12 12 3 12 12
504 4 9 14 4 9 14
504 4 9 14 9 4 14
520 4 10 13 4 10 13
520 4 10 13 4 13 10
520 4 10 13 10 4 13
520 4 10 13 10 13 4
528 4 11 12 4 11 12
528 4 11 12 4 12 11
560 5 8 14 5 8 14
560 5 8 14 8 5 14
585 5 9 13 5 9 13
585 5 9 13 5 13 9
585 5 9 13 9 5 13
585 5 9 13 9 13 5
588 6 7 14 6 7 14
588 6 7 14 7 6 14
600 5 10 12 5 10 12
600 5 10 12 5 12 10
600 5 10 12 10 5 12
600 5 10 12 10 12 5
605 5 11 11 5 11 11
624 6 8 13 6 8 13
624 6 8 13 6 13 8
624 6 8 13 8 6 13
624 6 8 13 8 13 6
637 7 7 13 7 7 13
637 7 7 13 7 13 7
648 6 9 12 6 9 12
648 6 9 12 6 12 9
648 6 9 12 9 6 12
648 6 9 12 9 12 6
660 6 10 11 6 10 11
660 6 10 11 6 11 10
660 6 10 11 10 6 11
660 6 10 11 10 11 6
672 7 8 12 7 8 12
672 7 8 12 7 12 8
672 7 8 12 8 7 12
672 7 8 12 8 12 7
693 7 9 11 7 9 11
693 7 9 11 7 11 9
693 7 9 11 9 7 11
693 7 9 11 9 11 7
700 7 10 10 7 10 10
700 7 10 10 10 7 10
700 7 10 10 10 10 7
704 8 8 11 8 8 11
704 8 8 11 8 11 8
720 8 9 10 8 9 10
720 8 9 10 8 10 9
720 8 9 10 9 8 10
720 8 9 10 9 10 8
720 8 9 10 10 8 9
720 8 9 10 10 9 8
729 9 9 9 9 9 9
Out of the 65 different configurations shown, there are only 25 different volumes, each with its own specific shape; that is, for example, 720 cm^3 is only from a shape of 8x9x10, regardless of which dimension has the 8 or the 9 or the 10 cm.
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Posted by Charlie
on 2016-03-03 11:31:38 |
computer solution
