Answers to last issue's Brain Teasers

1. Classic Old One: Three people go to a hotel. They pay Rs. 30 for a room, each person contributing an equal share of the rent. The owner suddenly remembers that the room rate is Rs. 25 only. He gives Rs. 5 to the bellboy to return to the people. The bellboy could not figure out how to return Rs. 5 equally to three people. So he returns Re. 1 each and keeps the remaining Rs. 2. Each person paid Rs. 10 and got back Rs. 1. So they paid Rs. 9 each. The total money they have paid is Rs. 9 X 3 = Rs. 27. The bellboy has pocketed Rs. 2, so this totals Rs. 29. Where is the missing Re. 1?

Ans: The short answer to this puzzle is that there is no missing rupee!  Let us look at the amounts involved. The people have paid Rs. 30 and got Rs. 3 back so they have paid Rs. (30-3)=Rs. 27 in all. On the other hand, the owner gets Rs. 25 and the bellboy keeps Rs. 2 so that is Rs.  (25+2)=Rs. 27, which is the same as the amount spent. Adding Rs. 27 to Rs. 2 to get the puzzling Rs. 29 does not make sense since one is spent and the other is earned.

2. Logic puzzle: There are four houses in a row where Asha, Binay, Chhaya, and Diwan live. Each house has a different colour, yellow, red, orange and white. They each like different things to drink with their morning breakfast: milk, coffee, tea and water. Can you tell who lives in which house and what he or she likes to drink, based on the following hints.
1. Diwan lives in the first house on the left.
2. Binay's house is red. 
3. The orange house is to the immediate left of the white house.
4. The owner of the orange house drinks coffee.
5. Diwan drinks tea.
6. The coffee and tea drinkers are not neighbours.
7. Chhaya likes water.
Ans: Let us look at this in a systematic fashion. Imagine 4 houses in a row. The left-most one is Diwan's (first statement). The second statement does not say much, so let us go to the next one: the orange (O) and white (W) houses are next to each other. There are three possibilities where this happens: OWXX, XOWX, XXOW, where X stands for an unknown colour.
Now look at statements 4 and 5. Diwan drinks tea but the owner of the orange house drinks coffee. Now we know that Diwan's house is on the left, so his house cannot be orange, and hence the combination OWXX is not possible.
So the two possibilities XOWX (with the orange and white houses in the middle) and XXOW (with the O and W on the right) are left. Since the first house is Diwan's, let us label it D, so we get DOWX or DXOW.
We know that Diwan (left-most house) drinks tea. Also the orange house owner drinks coffee. Now look at statement 6: The coffee and tea drinkers are not neighbours. This means D and the orange house cannot be adjacent. So the choice DOWX is not possible, so we are left with DXOW. 
Statement 2 says that Binay lives in a red (R) house, so X must be Binay. So Diwan lives in a yellow (Y) house. The houses, in order, are YROW. We know that Diwan and Binay live next to each other but we don't know who lives in the other two houses.
Let us go to statement 7: Chhaya likes water. The orange house owner likes coffee, so the owner cannot be Chhaya. So Chhaya lives in the white house. So Asha lives in the orange house.
Finally, it means Binay likes milk.
So, the order of colours of the houses is Yellow, Red, Orange, White (YROW). The order of owners is Diwan, Binay, Asha, Chhaya (DBAC). They like to drink, in order, tea, milk, coffee, and water.