Five friends in Timbuktu go to a local restaurant. They do not recognise any of the dishes on the Menu as they are not familiar with
such food but they are excited to try out. Each
one of them orders one dish, not necessarily distinct. The waiter brings the
dishes and places them in the middle, without saying which is which. At
this point, they may be able to tell the names of some of the dishes based on logical reasoning. For example, if two
people ordered the same dish, and everyone else ordered different
dishes, then the item for which two portions arrived can be told deterministically. They enjoyed the food a lot and were eager to try more of it next day.
They return to the restaurant two more times and followed the same experiment,
though with a new set of orders. After three meals, they have eaten all
nine dishes on the menu, and can tell which is which.
What pattern of ordering did they follow to fulfil this?
Scroll Down for answer..
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Scroll Down for answer..
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Let's say dished are marked 1,2,3 ..9. Then following table
lists down the dished ordered by each one of them and the last two columns
lists down the dishes they have tried till now and recognized respectively.
Person 1
|
Person 2
|
Person 3
|
Person 4
|
Person 5
|
Dish Tried
|
Dish Recognized
|
|
Dish Ordered 1st
Visit
|
1
|
2
|
2
|
3
|
4
|
1,2,3,4
|
2
|
Dish Ordered 1st
Visit
|
4
|
5
|
5
|
6
|
7
|
1,2,3,4,
5,6,7
|
2,5,4*
|
Dish Ordered 1st
Visit
|
1
|
7
|
8
|
8
|
9
|
1,2,3,4,
5,6,7,8,9
|
1,2,3,4,**
5,6,7,8,9
|
*
- They will recognize Dish 5 since two portions will arrive
- They will recognize Dish 4 since they know it is one of the dish they tried previous day and dish6 and 7 are new ones
**
- Dish 8 can be recognized since its two portion
- Dish 1 can be recognized since it matches one of the dishes ordered on first day
- Dish 3 can be recognized since it was ordered on Day1 and has not been repeated on Day2 or Day3
- Dish 6 can be recognized since it was ordered on Day2 but has not been repeated on Day3
- Dish 7 can be recognized since it was ordered on Day2 and has repeated on Day3
- Dish 2,5,4 are already recognized by Day 2
- Dish 9 can be recognized as all the other dishes on Day3 have been recognized.
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