Face of a large cube are painted with six different colours- Red , violet, yellow green, orange and blue. Green and violet are opposite to each other. Red and orange are opposite to each other. The cube is placed on a table with the yellow face touching the table and the orange face is towards the front. the cube is cut in to 210 identical pices by making least number of cuts. Out of the total cuts made the maximum number of cuts are made in horizonatl direction and the least number of cuts in the direction parallel to the violet face.
 
How many pieces have atmost one face painted?
 
Options are:
  1. 116. B. 124 C. 142. D. 154 

Dear Student,

This question is not based on the concept of probability. Let us assume that we cut x no. of cubes along a line. Thus the cubes which have atleast two face painted will be 12x-16Now, 210-12x+16 are number of cubes which have atmost one face painted.i.e. number of cubes which have atmost one face painted=226-12xIf, 226-12x=11612x=226-116=110 i.e. x=9.167If, 226-12x=12412x=226-124=102 i.e. x=8.5If, 226-12x=14212x=226-142=84 i.e. x=7If, 226-12x=15412x=226-154=72 i.e. x=6So the coorect answer is C or D.

Regards

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