Challenging Inequality problem 1

Solve the inequality


From G.C, 0.5<x< 2.81, x not equal to 2 (This is the easy part)

Hence solve


This is the HOT (Higher Order Thinking) part.

Method 1

Let f(x) =


Therefore f(x+2) =


f(x+2) is translation of f(x) by 2 units in the negative X direction.

Therefore, the solution is -1.5< x<0.81, x not equal to 0

This solution combines the concept of inequality and transformation of graph.

Method 2

Replace x by x+2.

Therefore 0.5<x+2< 2.81, x+2 not equal to 2

-1.5<x<0.81, x not equal to 0

Challenging Permutation question 2

Question: 6 adults and 3 children are sitting in a round table. Find the number of possible seating arrangement if none of the children sit together.

Solution: Choose 3 out of the 6 possible slots for the children to be seated between 2 adults, then multiply by 3! for the children permutation, then multiply by (6-1)! for the 6 adult circular permutation. Ans: 14400

Principle used: Slotting principle.

Challenging Permutation question 1

Q: There are five buildings. There are 4 different colours of paint. Each building must be painted with only 1 colour. Find the number of ways to paint all the 5 buildings if all 4 colours must be used.

Solution: 5 Choose 2 to have the same colour, then multiply by 4! for the colour permutation. Ans = 240

Principle used: Grouping principle.