Question

a triangular pyramid is built with 20 cannon balls as shown. Each cannon ball is labelled with one of A,B,C,D OR E. there are four cannon balls with each type of label. the pictures shows the labels on the Cannon balls on three of the faces of the pyramid. What is the label on the hidden cannon ball in the middle of the face? a) A. b) B. c) C. d) D. e) E​

Answer 1

Given : A triangular pyramid is built with 20 cannon balls, as shown. Each cannon ball is

labelled with one of A, B, C, D or E. There are four cannon balls with each type of label

The picture shows the labels on the cannon balls on three of the faces of the pyramid.

To Find : label on the hidden cannon ball in the middle of the fourth face

Solution:

Bottom layer has

DECA  , CBAD ,  AEBC

Here   C , A and D  are common   ( corners one )

middle ones are each once

A  = 3 - 1  - 2

B  = 2

C  = 3 - 1 = 2

D  = 2 - 1  = 1

E = 2

9 balls  at bottom layers are as  above

then

BED  , EAB  , DCE

here B ,  E and D  are common   ( corners one )

middle ones are each once

Hence   A  = 1   ,  B  = 1  , C   = 1  , D  = 1  ,   E  = 2

6  balls  at  2nd layer are as above

CA , BC , AB   these are  A = 1 , B = 1 , C = 1

3  balls  at  3rd  layer are as above

Next  D = 1

top vertex

in total A = 2 + 1 + 1  = 4  already uses

B = 2 + 1 + 1 = 4

C = 2 + 1 +  1 = 4

D = 1 + 1 + 1 = 3  only used

E = 2 + 2 = 4

Hence Left is D    ball

so   label on the hidden cannon ball in the middle of the fourth face is  D

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label on the hidden cannon ball in the middle of the fourth face

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