5 replies to this topic

[bhramarraj]

Five friends Anita, Bina, Chitra, Dimpy, & Ekta all have a habit of eating  fruits or sweets before and after their meals.

[1] Four friends eat Apple before or after their meals.
[2] Three friends eat orange before or after their meals.
[3] Two friends eat banana before and after their meals.
[4] One friend eats sweet before or after her meals.
[5] Either Anita & Bina, both or Chitr & Dimpy both eat banana before or after their meals.
[6] Of Bina & Chitra either both eat or neither eat orange before or after their meals.
[7] Dimpy and Ekta did not both eat apple before or after their meals (i.e. only one of them eats apple before or after her meals).

Now, with the help of above clues, you are required to tell, Who eats SWEETS.

[Pickett]

Spoiler for Answer

So, let's assume that neither Bina and Chitra ate oranges. This would mean Anita, Dimpy, and Ekta all ate oranges before their meal (clue 2). However, we know (from clue 7), that Anita, Bina, and Chitra all eat apples...so, if we assume that the person who eats sweets doesn't eat any fruits, we know that this cannot be true, because we then have everyone eating a fruit. Therefore, we know that both Bina and Chitra ate oranges.

So, we have this KNOWN so far:

Anita  - Apples
   Bina   - Apples, Oranges
   Chitra - Apples, Oranges

Going from there, unless I am missing something, I can see 2 ways that Dimpy could be the sweet eater, and 4 ways that Ekta could be the sweet eater...:
DIMPY:

Anita  - Apples, Bananas
   Bina   - Apples, Bananas, Oranges
   Chitra - Apples,          Oranges
   Dimpy  - SWEETS!!
   Ekta   - Apples,          Oranges

Anita  - Apples, Bananas, Oranges
   Bina   - Apples, Bananas, Oranges
   Chitra - Apples,          Oranges
   Dimpy  - SWEETS!!
   Ekta   - Apples

EKTA:

Anita  - Apples, Bananas, Oranges
   Bina   - Apples, Bananas, Oranges
   Chitra - Apples,          Oranges
   Dimpy  - Apples
   Ekta   - SWEETS!!!

Anita  - Apples, Bananas
   Bina   - Apples, Bananas, Oranges
   Chitra - Apples,          Oranges
   Dimpy  - Apples,          Oranges
   Ekta   - SWEETS!!!

Anita  - Apples,          Oranges
   Bina   - Apples,          Oranges
   Chitra - Apples, Bananas, Oranges
   Dimpy  - Apples, Bananas
   Ekta   - SWEETS!!!

Anita  - Apples
   Bina   - Apples,          Oranges
   Chitra - Apples, Bananas, Oranges
   Dimpy  - Apples, Bananas, Oranges
   Ekta   - SWEETS!!!

Edited by Pickett, 14 June 2012 - 03:34 PM.

[curr3nt]

Spoiler for I think I got it...

Bina ate sweets.

From #5 we have two sets:
A - b A -
B - b B -
C - C - b
D - D - b
E - E -

From # 6 we have four sets:
bo - A - b o - A -
b - B - bo - B - o
- C - o b - C - bo
o - D - bo - D - b
o - E - o - E -

Fill in the four apples where allowed then remove those that break #7:
bo - A - ab a o - A - a
ab - B - bo a - B - a o
a - C - a o ab - C - bo
a o - D - a bo - D - ab
a o - E - a a o - E - a
That leaves the third set where Bina had the sweets.

Edit for formatting...I give up trying to get the formatting right...

Edited by curr3nt, 14 June 2012 - 03:55 PM.

[TripleOption]

Spoiler for

Oranges Bananas Apples Anita YES NO YES Bina NO NO YES Chitra NO YES YES Dimpy YES YES NO Ekta YES NO YES Bina is the answer

Edited by TripleOption, 14 June 2012 - 07:12 PM.

[MikeD]

Spoiler for

Bita ate the sweets.

I assumed that each friends would only eat two items.
(A = Anita, B = Bina, C = Chitra, D = Dimpy and E = Ekta)

From clue 7 either D or E ate an apple so A, B, C must have eaten an apple (four apples eaten)
From clue 6 either A and B, or C and D ate banana.
From clue 8 either B, C and a third person ate oranges, or A, D and E ate oranges.

If B and C ate oranges then both friends would have eaten two items, therefore making it impossible for clue 6 to be true.
Since clue six is assumed true, B and C could not have eaten oranges, leaving A, D and E.
Making D now eating two item, So D can't ate the other apple (clue 6) so it must be E who eats it.

So adding it all up we have:
A Apple & Orange
B Banana
C Apple & Banana
D Banana & Orange
E Apple & Orange

Leaving B to have the sweets.

[bhramarraj]

Spoiler for

Bita ate the sweets.

I assumed that each friends would only eat two items.
(A = Anita, B = Bina, C = Chitra, D = Dimpy and E = Ekta)

From clue 7 either D or E ate an apple so A, B, C must have eaten an apple (four apples eaten)
From clue 6 either A and B, or C and D ate banana.
From clue 8 either B, C and a third person ate oranges, or A, D and E ate oranges.

If B and C ate oranges then both friends would have eaten two items, therefore making it impossible for clue 6 to be true.
Since clue six is assumed true, B and C could not have eaten oranges, leaving A, D and E.
Making D now eating two item, So D can't ate the other apple (clue 6) so it must be E who eats it.

So adding it all up we have:
A Apple & Orange
B Banana
C Apple & Banana
D Banana & Orange
E Apple & Orange

Leaving B to have the sweets.

Excelent....!!!! I also did not solve it with such simplicity. My original solution is

Spoiler for My original solution

From [1] & [7]: Four apple eater are (i) A, B, C, & D OR (ii) A, B, C, & E
Similarly from [2] & [6]: Three orange eater are either (iii) B, C, & A (iv) B, C & D (v) B, C, & E OR (vi) A, D, & E
From [3} & [5]: Two banana eaters are (vii) A & B OR (viii) C & D.
From above Different sets are as under:
SET-I: (i), (iii), (vii) : B is three fruits eater. So not possible.
SET-II: (i), (iv), (vii) : B is three fruits eater. So not possible.
SET-III: (i), (v), (vii) : B is three fruits eater. So not possible.
SET-IV: (i), (vi), (vii): A is three fruits eater. So not possible.
SET-V: (ii), (iii), (vii): B is three fruits eater. So not possible.
SET-VI: (ii), (iv), (vii): B is three fruits eater. So not possible.
SET-VII: (ii), (v), (vii): B is three fruits eater. So not possible.
SET-VIII: (ii), (vi), (vii): A is three fruits eater. So not possible.
SET-IX: (i), (iii), (viii): C is three fruits eater. So not possible.
SET-X: (i), (iv), (viii): C is three fruits eater. So not possible.
SET-XI: (i), (v), (viii): C is three fruits eater. So not possible.
SET-XII: (i), (vi), (viii): D is three fruits eater. So not possible.
SET-XIII: (ii), (iii), (viii): C is three fruits eater. So not possible.
SET-XIV: (ii), (iv), (viii): C is three fruits eater. So not possible.
SET-XV: (ii), (v), (viii): C is three fruits eater. So not possible.
SET-XVI: (ii), (vi), (viii): C is three fruits eater. So not possible.
LASTLY only set possible is:
SET-XVIII: (ii), (vi), (viii): All but B, eat two fruits as under
A & E eat Apple + Orange
C eats Apple + Banana
D eats Orange + Banana
B eats Apple.
Therefore B eats SWEETS.