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Grid Puzzles

Logic puzzles can get complicated, and keeping track of information while you're sleuthing is no easy task. See how grids can help you efficiently deduce your way to the truth.

Level 2

Place each of the digits \(1,2,3,\ldots,8\) in the grid above so that all of the equations are true.

Give your answer as the numbers from left-to-right and then top-to-bottom. For example, if you filled in the grid (incorrectly) as shown below, your answer would be \(32541876.\)

One evening there was a murder in the home of a father, a mother, their son, and their daughter.

One of these four people murdered one of the others. One other member of the family witnessed the crime. The other one helped the murderer.

These are the things we know for sure:

  1. The witness and the one who helped the murderer were not of the same sex.
  2. The oldest person and the witness were not of the same sex.
  3. The youngest person and the victim were not of the same sex.
  4. The one who helped the murderer was older than the victim.
  5. The father was the oldest member of the family.
  6. The murderer was not the youngest member of the family.

Who was the murderer?

Aaron, Calvin, David, and Peter each live in one of 4 adjacent townhouses in a row, each of a single color. Each owns one pet and imbibes one kind of drink.

  1. Aaron owns the dog.
  2. The bird lives in the red house.
  3. Calvin lives in the blue house.
  4. David does not live in the red house.
  5. The cat lives where the milk drinker lives.
  6. Either the fish lives next to the cat or the bird lives next to the coffee drinker.
  7. If the dog lives in the green house, then the cat lives next to the blue house.
  8. If Peter owns the fish, then either Calvin owns the bird or else David owns the cat.
  9. The tea drinker lives two houses away from the coffee drinker.
  10. The red house resident drinks water if and only if the yellow house resident drinks milk.

Who owns the fish?

Note: Color of residences as shown in photograph have nothing to do with this problem. Also, any pet "owned" is presumed to live in the same place as the owner lives.

Sandip, Tracy, Jamal, and Sheng are best friends who work together everyday at a banana stand. Since they are so close, their happiness on any given day depends on the happiness of the other three people on the previous day. Suppose they behave as follows:

  • Sheng is happy today only if Tracy and Jamal were both happy yesterday.
  • Jamal is happy today only if Sandip or Sheng (or both) were happy yesterday.
  • Sandip enjoys watching Sheng cry, so Sandip is happy today only if Sheng was sad yesterday.
  • Tracy is happy today only if Tracy was happy yesterday, meaning she has an independent streak.

Suppose that on day 1, all four of the friends are sad. After a few days, the friends reach a stable emotional state that repeats itself. What is the emotional state of each person in this repeating state?

Pop Quiz! Submit your answers, in order, to Questions 1-4.

Q1. Which is the first question where c) is the correct answer?

a) Q3
b) Q4
c) Q1
d) Q2

Q2. Which is the first question where a) is the correct answer?

a) Q4
b) Q2
c) Q3
d) Q1

Q3. Which is the first question where d) is the correct answer?

a) Q1
b) Q2
c) Q4
d) Q3

Q4. Which is the first question where b) is the correct answer?

a) Q2
b) Q4
c) Q3
d) Q1

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