Amit, Bharati, Cheryl, Deepak and Eric are five friends sitting in a…

2024

Amit, Bharati, Cheryl, Deepak and Eric are five friends sitting in a restaurant. They are wearing caps of five different colours — yellow, blue, green, white and red. Also they are eating five different snacks — burgers, sandwiches, ice cream, pastries and pizza. I. The person wearing a red cap is eating pastries. II. Amit does not eat ice cream and Cheryl is eating sandwiches. III. Bharati is wearing a yellow cap and Amit wearing a blue cap. IV. Eric is eating pizza and is not wearing a green cap. Who among the following friends is having ice cream?

  1. A.

    Amit

  2. B.

    Bharati

  3. C.

    Cheryl

  4. D.

    Deepak

Attempted by 2 students.

Show answer & explanation

Correct answer: B

This is a constraint-satisfaction puzzle: each of the five friends has exactly one cap colour and one snack, and every clue removes at least one impossible combination. Fix the attributes that a clue states directly first, then use the remaining clues to eliminate combinations one at a time until every person's colour and snack are fixed.

  1. Clue III directly fixes two people: Bharati wears yellow and Amit wears blue.

  2. The three remaining colours — green, white, red — belong to Cheryl, Deepak and Eric. Clue IV says Eric does not wear green, so Eric wears white or red.

  3. If Eric wore red, clue I would force him to eat pastries, but clue IV already fixes Eric's snack as pizza — a contradiction. So Eric wears white, leaving green and red for Cheryl and Deepak.

  4. Clue II fixes Cheryl's snack as sandwiches. If Cheryl wore red, clue I would force her snack to pastries, contradicting sandwiches. So Cheryl wears green, and Deepak wears red.

  5. Since Deepak wears red, clue I fixes his snack as pastries.

  6. Only burgers and ice cream remain, for Amit and Bharati. Clue II says Amit does not eat ice cream, so Amit eats burgers and Bharati eats ice cream.

Checking all four clues against this final assignment confirms consistency: the red-cap wearer (Deepak) eats pastries (clue I); Amit does not have ice cream and Cheryl has sandwiches (clue II); Bharati is yellow and Amit is blue (clue III); Eric has pizza and is not green (clue IV). Every condition holds, and Bharati is the one eating ice cream.

Reference working table:

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