Five boys A, B, C, D and E eat five different types of food F1, F2, F3, F4 and F5 (not necessarily in the same order). Each also likes a bird named B1, B2, B3, B4 and B5 (not necessarily in the same order). B eats F2. A does not like B3. E eats F1 but does not like B1 or B2. C does not eat F4 but likes B5. The one who eats F3 likes B3. B does not like B2. Which of the following statements are correct? I. A likes B2. II. C eats F5. III. E likes B4.
Analyzing the Logical Reasoning Puzzle
This problem requires us to use the given clues to deduce which boy eats which food and likes which bird. We have five boys (A, B, C, D, E), five foods (F1, F2, F3, F4, F5), and five birds (B1, B2, B3, B4, B5). Each boy is uniquely paired with one food and one bird.
Step-by-Step Deduction
Let's build a table to keep track of the information and deductions as we go through the clues:
| Boy | Food | Bird |
|---|---|---|
| A | ? | ? |
| B | ? | ? |
| C | ? | ? |
| D | ? | ? |
| E | ? | ? |
Now let's process the clues:
- Clue 1: B eats F2. We can fill this in the table.
- Clue 3: E eats F1 but does not like B1 or B2. We fill in E's food. We also know E's bird is not B1 or B2.
- Clue 4: C does not eat F4 but likes B5. We fill in C's bird.
| Boy | Food | Bird |
|---|---|---|
| A | ? | ? |
| B | F2 | ? |
| C | Not F4 | B5 |
| D | ? | ? |
| E | F1 | Not B1, Not B2 |
- From Clue 3, E eats F1 and does not like B1 or B2. Remaining birds are B3, B4, B5. C likes B5, so E cannot like B5. Thus, E likes B3 or B4.
- Clue 5: The one who eats F3 likes B3. This gives us a pair (F3, B3).
- Clue 2: A does not like B3. Since the person who eats F3 likes B3, A does not eat F3 either.
- Consider E again. E eats F1. If E liked B3, then according to Clue 5, E would eat F3. But E eats F1. So E cannot like B3. Since E likes B3 or B4, and cannot like B3, E must like B4.
| Boy | Food | Bird |
|---|---|---|
| A | Not F3 | Not B3 |
| B | F2 | ? |
| C | Not F4 | B5 |
| D | ? | ? |
| E | F1 | B4 |
- Now we use the (F3, B3) pair (Clue 5). Which boy eats F3 and likes B3?
- A does not like B3, so A is not the (F3, B3) boy.
- B eats F2, so B is not the (F3, B3) boy.
- C likes B5, so C is not the (F3, B3) boy.
- E eats F1 and likes B4, so E is not the (F3, B3) boy.
| Boy | Food | Bird |
|---|---|---|
| A | Not F3 | Not B3 |
| B | F2 | ? |
| C | Not F4 | B5 |
| D | F3 | B3 |
| E | F1 | B4 |
- Remaining foods are F4, F5. Remaining birds are B1, B2. Boy Food Bird Assignments so far: (E, F1, B4), (B, F2, ?), (D, F3, B3), (C, ?, B5), (A, ?, ?).
- Remaining boys for food/bird: A, B, C. Remaining foods: F4, F5. Remaining birds: B1, B2.
- Clue 6: B does not like B2. Since B needs a bird from the remaining list (B1, B2) and does not like B2, B must like B1.
| Boy | Food | Bird |
|---|---|---|
| A | Not F3 | Not B3 |
| B | F2 | B1 |
| C | Not F4 | B5 |
| D | F3 | B3 |
| E | F1 | B4 |
- Remaining bird is B2. The remaining boy without a bird is A. So, A must like B2.
| Boy | Food | Bird |
|---|---|---|
| A | Not F3 | B2 |
| B | F2 | B1 |
| C | Not F4 | B5 |
| D | F3 | B3 |
| E | F1 | B4 |
- Remaining foods are F4, F5. Remaining boys for food are A, C. C does not eat F4 (Clue 4). So, C must eat F5.
- The only remaining food is F4, and the only remaining boy without food is A. So, A must eat F4.
The final complete assignment is:
| Boy | Food | Bird |
|---|---|---|
| A | F4 | B2 |
| B | F2 | B1 |
| C | F5 | B5 |
| D | F3 | B3 |
| E | F1 | B4 |
Evaluating the Statements
Now let's check the given statements based on our final table:
- I. A likes B2. Looking at the table, A likes B2. This statement is Correct.
- II. C eats F5. Looking at the table, C eats F5. This statement is Correct.
- III. E likes B4. Looking at the table, E likes B4. This statement is Correct.
All three statements (I, II, and III) are correct based on our deductions.
Important Questions from Box Puzzle
Five boxes B1, B2, B3, B4 and B5 are placed one above the other in racks. The lowermost rack is numbered as one and just above the lowermost is numbered as two and so on. Each box is coloured with different colour such as L1, L2, L3, L4 and L5 (not necessarily in the same order). Two boxes are placed between L2 coloured box and L5 coloured box. Box B1 is not placed immediately above box B3. Box B4 is placed in the top most rack. L1 coloured box is placed immediate above L5 coloured box. Box B3 is coloured with L4. L5 coloured box is placed above L4 coloured box. Box B2 is coloured with L1. Which of the following boxes are placed immediately above and immediately below B5 box respectively?
J, K L, M, N and O are six teachers. Each one teaches a different subject out of Hindi, English, Math, Science, Social Science and Arts, NOT necessarily in the same order. Each of them teaches on only one day, from Monday to Saturday, NOT necessarily in the same order. J teaches Arts on Saturday. L teaches neither English nor Social Science, but he teaches on Thursday. Wednesday is reserved for Maths taught by K. O teaches Science a day before N. Social Science is taught a day before Arts.
Which subject is taught on the day between Thursday and Saturday?
Branches of five banks A,B,C,D and E are as follows:
1. A, B and C are in Indore and Bhopal.
2. A, B and E are in Indore and Gwalior
3. B, C and D are in Raipur and Bhopal.
4. A, E and D are in Gwalior and Jabalpur
5. C,E and D are in Raipur and Jabalpur
Branch of which bank is in all places except Gwalior?
Which box is placed at the top?
What is the sum of pencils in box A and box P?
