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Blocks Boxes

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There are eight 8-blocks boxes that contains different
numbers of blocks inside. Stacked into 2 x 2 x 2 for stability.

The Blocks contents of the Boxes are as follows:
Top Front boxes = Bottom Front boxes
Top Rear boxes = Bottom Rear boxes
Top Left boxes = Bottom Left boxes = Rear Right boxes
Top Right boxes = Bottom Right boxes=Front Left boxes
Front Right boxes = 6 & Rear Left boxes = 12

Can you label all the boxes by the number of blocks inside ?

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2 answers to this question

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Posted · Report post

There is either some info missing or I have misunderstood the question. I am getting 2 solutions that satisfy the conditions:

Lets say the boxes are arranged as:

c d

a b

g h

e f

Then;

a+b = e+f

c+d = g+h

a+c = g+e = d+h

d+b = h+f = a+e

b+f = 6

c+g = 12

Subtract 1 and 3; b-c = f-g

The, b+g = c+f

b+g+c+f = 18

Therefore, b+g = c+f = 9

Also, substract 2 and 3

then c-h = h-e

c+e = 2h

Now b+g = 9, there are 4 possibilities; 1/5; 5/1; 2/4; 4/2

All the conditions are satisfied with the first 2 possibilities as below:

b f c g e h a d 1 5 4 8 2 3 6 7

b f g c e h a d 5 1 4 8 6 7 2 3

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Posted · Report post

Well solved (probably symmetric) :thumbsup:

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