Answers to last issue's Brain Teasers

1. Can you complete the grid such that every row and column contains the
digits 1 to 6.
All squares that are connected contain the same digit.

Hint: Start with the three connected squares that contain the third column on the bottom row.

2. During a recent expedition, three intrepid adventurers were left
stranded in the middle of the desert with only a crate full of apples.

During the night, Alan woke up and decided to hide his share of the
apples and hid a third, then promptly fell asleep again.

Brian woke up shortly after and also decided to hide a third of the
remaining apples and he also dozed back to sleep.

Finally, Charlie woke up and seeing the others were asleep, took a third
of what was left.

Of course none of the adventurers knew of the other's antics, so, in the
morning, they shared the remaining apples, each receiving sixteen. How
many apples were in the crate originally?

Ans: 162.
To work these numbers out, we start at the end and work backwards.  At the end there were 16 apples for each person, therefore there were 48 apples in all. 
Charlie removed 1/3 of the apples he saw, and left 2/3, but we know that there were 48 left, so there must have been (3/2)x48=72 apples before he removed his share.
Brian removed 1/3 of what he saw, but now we know that the 2/3 of the total at that time was 72. Again, there must have been (3/2)x72=108 apples before he removed his share.
Similarly, Alan removed 1/3, leaving 108, so there must have been (3/2)x108=162 apples in the first place.
So Alan hid (1/3)x162=54 apples as his share, leaving 108. Then Brain hid (1/3)x108=36, leaving 72. Finally, Charlie hid (1/3)x72=24, leaving 48 apples which were then available for them to share equally in the morning.

3. 

Ans: This is a trick question: you must be careful of what you're adding.
Originally, they paid Rs. 30, they each received back Rs. 1, they now have only paid Rs. 27.
Of this Rs. 27, Rs. 25 went to the manager for the room and Rs. 2 went to the bellboy.