perplexus.info :: Shapes : Box Volume Baffle

Box Volume Baffle (Posted on 2014-11-05)

The respective length, breadth and height of the rectangular cuboid R₁ is A+2, B+2 and C+2 and the respective length, breadth and height of the rectangular cuboid R₂ is A, B and C.

It is known that:

(i) The volume of R₁ is precisely twice that of R₂, and:
(ii) Each of A, B and C is a positive integer with A ≤ B ≤ C

Determine the maximum value of C.

No Solution Yet Submitted by K Sengupta

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

No Subject

| Comment 3 of 5 |

For tot = 3 To 3000

For a = 1 To tot / 3

For b = a + 1 To (tot - a) / 2

c = tot - a - b

area2 = a * b * c

area1 = (a + 2) * (b + 2) * (c + 2)

If area1 = 2 * area2 Then

Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf

DoEvents

End If

Next tot

finds

a b c

6 8 10

6 7 12

5 8 14

4 12 14

5 7 18

4 10 18

4 9 22

5 6 28

4 8 30

3 20 22

3 18 25

3 16 30

3 15 34

3 14 40

4 7 54

3 13 50

3 12 70

3 11 130

The largest c here is 130, and it looks like solutions stop here.

Posted by Charlie on 2014-11-06 08:19:07

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