Directions for question :Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours. The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.It was also known that :a) The stick with the red colour was opposite to the stick with the blue colourb) There were exactly two sticks whose both ends had colours whose names started with the same letterc) The stick with the grey colour was adjacent to the stick with the white colourd) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue coloure) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colourf) The stick with the white colour was opposite to the stick with the green colourQuestion :What was the colour of the bottom end of the stick having brown colour at the top end ?Option: 1  White   Option: 2 Yellow Option: 3 Black  Option: 4 Grey

From (b) we know that there were exactly two sticks whose both ends had colours whose names started with the same letter.

The only two possible combinations could be (i) Pink (top) and Purple (bottom) and (ii) Black (top) and Blue (bottom)

From (a) and (d), we could get two cases of arrangement of the sticks as shown below :

Point (e) says that the stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour

Green was the colour of the top of a stick, while purple and grey were colours of the bottom of two different sticks. The purple bottomed stick had pink as the colour of the top. That meant that the stick with pink colour at the top was adjacent to the sticks with green at the top and grey at the bottom.

Hence, the two cases of arrangement of the sticks change to as shown below :

Now, from (c) we get to know that the stick with the grey colour was adjacent to the stick with the white colour

White was the colour of a bottom end. So in both the cases white had to be the colour of the bottom end of the stick with brown colour at the top

Hence the colours of orange or yellow could either be the bottom colours of the sticks with top painted cyan and green respectively, or vice versa

Hence, the final two cases of arrangements possible are as given below :

Hence, the colour of the bottom end of the stick having brown colour at the top end is white