Three children, Sam, John and Ann, are eating icecream. Each child eats a different flavour from available flavours, namely Chocolate, Strawberry, Butterscotch and Vanilla.
* Sam does not eat Vanilla.
* John does not eat Strawberry.
* Ann never eats Butterscotch.
* Chocolate and Butterscotch are not eaten together.
* Vanilla and Chocolate are eaten together.
Who eats what flavour from the available options?
1. Sam - Strawberry, John - Butterscotch, Ann - Chocolate
2. Sam - Strawberry, John - Chocolate, Ann - Vanilla
3. Sam - Chocolate, John - Vanilla, Ann - Strawberry
4. Sam - Butterscotch, John - Chocolate, Ann - Strawberry
Which of the above combinations could be correct?
- A2 and 4
- B1 and 3
- C2 and 3
- D3 and 4
Solution & Step-by-step Explanation
Let's analyze the given conditions against the provided combinations:
* Condition: "Chocolate and Butterscotch are not eaten together." This means no two children can eat Chocolate and Butterscotch in the same valid scenario combination. Wait, the phrasing "are not eaten together / are eaten together" refers to the chosen set of 3 flavors being consumed by the group simultaneously.
* Let's check rule: "Vanilla and Chocolate are eaten together." This means if one person eats Vanilla, another person MUST eat Chocolate within that valid option, or vice versa.
Let's test each combination:
* Combination 1: Sam - Strawberry, John - Butterscotch, Ann - Chocolate.
Flavors used: Strawberry, Butterscotch, Chocolate.
Violation: "Vanilla and Chocolate are eaten together" is violated because Chocolate is present but Vanilla is not. So 1 is invalid.
* Combination 2: Sam - Strawberry, John - Chocolate, Ann - Vanilla.
Flavors used: Strawberry, Chocolate, Vanilla.
Check constraints:
* Sam does not eat Vanilla (True, eats Strawberry)
* John does not eat Strawberry (True, eats Chocolate)
* Ann never eats Butterscotch (True, eats Vanilla)
* Chocolate and Butterscotch not together (True, no Butterscotch)
* Vanilla and Chocolate are together (True, both present).
Hence, Combination 2 is valid.
* Combination 3: Sam - Chocolate, John - Vanilla, Ann - Strawberry.
Flavors used: Chocolate, Vanilla, Strawberry.
Check constraints:
* Sam does not eat Vanilla (True, eats Chocolate)
* John does not eat Strawberry (True, eats Vanilla)
* Ann never eats Butterscotch (True, eats Strawberry)
* Chocolate and Butterscotch not together (True)
* Vanilla and Chocolate are together (True, both present).
Hence, Combination 3 is valid.
* Combination 4: Sam - Butterscotch, John - Chocolate, Ann - Strawberry.
Flavors used: Butterscotch, Chocolate, Strawberry.
Violation: Chocolate and Butterscotch are present together, which violates "Chocolate and Butterscotch are not eaten together". Also, Vanilla and Chocolate are not together. So 4 is invalid.
Therefore, combinations 2 and 3 could be correct.
* Condition: "Chocolate and Butterscotch are not eaten together." This means no two children can eat Chocolate and Butterscotch in the same valid scenario combination. Wait, the phrasing "are not eaten together / are eaten together" refers to the chosen set of 3 flavors being consumed by the group simultaneously.
* Let's check rule: "Vanilla and Chocolate are eaten together." This means if one person eats Vanilla, another person MUST eat Chocolate within that valid option, or vice versa.
Let's test each combination:
* Combination 1: Sam - Strawberry, John - Butterscotch, Ann - Chocolate.
Flavors used: Strawberry, Butterscotch, Chocolate.
Violation: "Vanilla and Chocolate are eaten together" is violated because Chocolate is present but Vanilla is not. So 1 is invalid.
* Combination 2: Sam - Strawberry, John - Chocolate, Ann - Vanilla.
Flavors used: Strawberry, Chocolate, Vanilla.
Check constraints:
* Sam does not eat Vanilla (True, eats Strawberry)
* John does not eat Strawberry (True, eats Chocolate)
* Ann never eats Butterscotch (True, eats Vanilla)
* Chocolate and Butterscotch not together (True, no Butterscotch)
* Vanilla and Chocolate are together (True, both present).
Hence, Combination 2 is valid.
* Combination 3: Sam - Chocolate, John - Vanilla, Ann - Strawberry.
Flavors used: Chocolate, Vanilla, Strawberry.
Check constraints:
* Sam does not eat Vanilla (True, eats Chocolate)
* John does not eat Strawberry (True, eats Vanilla)
* Ann never eats Butterscotch (True, eats Strawberry)
* Chocolate and Butterscotch not together (True)
* Vanilla and Chocolate are together (True, both present).
Hence, Combination 3 is valid.
* Combination 4: Sam - Butterscotch, John - Chocolate, Ann - Strawberry.
Flavors used: Butterscotch, Chocolate, Strawberry.
Violation: Chocolate and Butterscotch are present together, which violates "Chocolate and Butterscotch are not eaten together". Also, Vanilla and Chocolate are not together. So 4 is invalid.
Therefore, combinations 2 and 3 could be correct.