IMAT 2016 Q3 [Painted Tins]

Below is a picture of a biscuit tin with four identical sides. A set of these tins is to be made that are all distinguishable from each other by colour alone. The manufacturer will paint each of the four sides either red or blue. The top and bottom are not painted.

image

What is the greatest number of different tins that can be made?

A. 6
B. 7
C. 8
D. 4
E. 5

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Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

Approach: find all the possible combinations of red and blue, while considering that the tin could be all red or all blue. Also, note that some combinations will be the same depending on orientation.

Let ‘R’ stand for red side, and ‘B’ stand for blue side.

  1. B B B B

  2. R R R R

  3. R R B B

  4. B R B R

  5. B B B R

  6. R R R B

Anything else?

What about R B B R? No, this is the same as R R B B. Remember this is a tin with 4 sides.

Since there are no other possible combinations, 6 is the max possible.

\fcolorbox{red}{grey!30}{Therefore the answer is A, $6$.}