19th GB !

Tuesday, March 31, 2009

Noted @ 6:36 PM.

Hi Sec 3,

Here is the solution for Exercise 1:

Question:

There are five houses, each of a different colour and inhabited by people of different nationalities, with different pets, drinks, and pastimes.
The English live in the Red house.
The Spaniards own the Dog.
Coffee is drunk in the Green house.
The Ukrainians drink Tea.
The Green house is immediately to the right (your right) of the Ivory house.
The Chess players own Snails.
Scrabble is played in the Yellow house.
Milk is drunk in the Middle house.
The Norwegians live in the First house on the Left.
People who play Cribbage live in the house next to the people who own a pet Fox.
Scrabble is played in the house next to the house where the Horse is kept.
The Bridge players drink Orange Juice.
The Japanese play Monopoly.
The Norwegians live next to the Blue house.

Who drinks water? And who owns the Zebra?

Answers:

We know for a fact that Norwegians live in the far left House # 1 (Given 10).
We know for a fact that the house next to the Norwegians # 2 is Blue (Given 15).
We know for a fact that Milk belongs in the middle House # 3 (Given 9).
We know for a fact that the Green house is immediately to the right of the Ivory house (Given 6) so # 1 cannot be Ivory because Blue to the right of it (see point # 2) nor can # 2 because it is Blue, nor # 5 because there is nothing to the right of it, so it follows that the Ivory house has to be # 3 or # 4 and Green has to be #4 or #5 (Given 6).
The English live in the Red house (Given 2). This mean that # 1 cannot be Red (the Norwegians live in # 1), or Blue (see point 2), or Ivory, or Green, (see point 4) so # 1 must be Yellow.
We know for a fact that Scrabble is played in the Yellow House # 1 (Given 8).
We know for a fact that Scrabble is played in the house next to the house where the Horse is kept (Given 12) so the Horse must live in House # 2 which is the only house next to # 1 which is where they play Scrabble (see point 6).
The drink in House # 1 cannot be Tea because the Ukrainians drink tea (Given 5) and the Norwegians live in # 1 (Given 10) or Orange Juice because Bridge is played while drinking Orange Juice (Given 13) and Scrabble is the game in house # 1 (see point 6), or Milk because it belongs in House # 3 (see point 3) or Coffee because it belongs in the Green house (Given 4) and House # 1 is Yellow (see point 5). That means the only drink left for House # 1 is Water
THEREFORE THE NORWEGIANS MUST DRINK WATER.
House # 2 is Blue (see point 2) so the English can't live there because they live in a Red house.
Horse lives in House # 2 (see point 7) so the Spaniards can't live there because they have a Dog (Given 3).
Since we know the Norwegians live in # 1 (see point #1) only the Tea drinking Ukrainians (Given 5) or the Monopoly playing Japanese (Given 14) could live in House # 2.
The people who play Cribbage live next to the people who own a pet Fox (Given 11) so they can be in any house except # 1 where they play Scrabble (see point 6).
Bridge players drink Orange Juice (Given 13) so can't be in House # 1 where they drink Water (see point 9) or House # 3 where they drink Milk (see point 3).
The Bridge playing Orange Juice drinkers cannot live in House # 2 because if they did the Tea Drinking Ukrainians and the Monopoly playing Japanese could not live there, which would mean no one could live there (see points 10, 11, 12).
Since the people in House # 2 can't be Orange Juice drinkers (see point 15) or Water drinkers (see point 9) or Milk drinkers (see point 3) or Coffee drinkers who live in a Green house (Given 4 and point 2) they must be Tea drinking Ukrainians (Given 5).
Since they are not Orange Juice drinking Bridge players (see point 15) or Monopoly playing Japanese (see points 16) or Scrabble players (see point 6) or Chess playing Snail owners (see Given 7) because they own a horse (see point 7) they must play Cribbage in House # 2.
In summary House # 2 is Blue, has the Ukrainians living in it with a Horse, drinking Tea and playing Cribbage.
Since they play Cribbage in House # 2 then only the people in house # 1 or # 3 can live with a Fox (Given 11)
If we assume the Fox is in House # 3 then the Zebra can't be there (Given # 1) or the Spanish who own a Dog (Given 3) or the Chess playing Snail owners (Given 7). Since they drink Milk in House # 3 (Given 9) they cannot be Orange Juice drinking Bridge players (Given 13) so with Scrabble being played in House # 1 (see point 6) and Cribbage in House # 2 (see point 18) the only pastime left available to house # 3 is Monopoly which means that the Japanese live there (Given 14), which would mean that the house must be Ivory because, it can't be Yellow (see point 5), or Blue (see point 2) or Red which is the colour of the English house (Given 2) or Green (See point 4).
In summary if the Fox lives in House # 3 then so do the Japanese who drink Milk and play Monopoly and the house is Ivory in colour. It follows then that House # 4 is Green (Given 6) and they drink Coffee there (Given 4) so they cannot play Bridge there because they cannot drink Orange Juice (Given 13). Nor can the English live there because their house is Red (Given 2). Since it also cannot be the Norwegians living there (Given 10), or the Ukrainians (see point 16) or the Japanese (see point 21) who live there, it must be the Dog owning Spaniards, which means it can't be the Snail owning Chess players (Given 7) BUT that means there is no pastime for House # 4 - It can't be Scrabble (see point 6) or Cribbage (see point 17) or Monopoly (see point 20), Bridge or Chess (see point 21). Therefore the Fox can't live in House # 3 (The assumption made in point 20 is not valid.Points 20 - 21 (Not Valid)
The Fox must live in House # 1 with the Norwegians (see points 19, 20, 21, and Given 10 and 11).
If we now assume House # 4 is Ivory then house # 3 must be Red with the English living there (Given 2) because it is the only colour left available to it. It can't be Yellow (see point 5), or Blue (see point 2), or Green, # 5 would have to be Green (Given 6). Since we now believe that the English must live in # 3, Monopoly can't be played there because it is played by the Japanese (Given 14) or a Dog living there because it is owned by the Spaniards (Given 3). So in House # 3 they must play Chess, because it is the only pastime left for them and own Snails (Given 7), which means they can't have Snails or play Chess in house # 4 or # 5.
In summary, if we assume House # 4 is Ivory then the English live with their Sails in House # 3, which is Red. They play Chess and drink Milk.
If House # 4 is assumed Ivory then House # 5 is Green and they drink Coffee there (Given 6 and 4) which means that they can not drink Orange Juice and play Bridge there, which means that they must play Bridge and drink Orange Juice in House # 4 because it is the only house left without a drink.
Since they drink Orange Juice and play Bridge in House # 4 they can not be the Monopoly playing Japanese, which means they must be the Spaniards who own a Dog. It follows that since we know that living in House # 1 are the Norwegians (Given 10), House # 2 are the Ukrainians (see point 16), House # 3 are the English (see point 23), House # 4 are the Spanish (see point 26), the Monopoly playing Japanese must live in House # 5.
This means that the Fox lives in House # 1 (see point 22 ) with the Norwegians (Given 10), the Horse in House # 2 (see point 7) with the Ukrainians (see point 16), the Sails live in House # 3 (see point 23) with the English (see point 23), the Dog in House # 4 (see point 26) with the Spaniards (Given 3), and that the ZEBRA MUST LIVE IN HOUSE # 5 WITH THE JAPANESE.