Six people were in a room together, when suddenly the lights went out. When the lights came back on, Fred Albert's wallet was missing!
Detectives have investigated, they have questioned the suspects, the witnesses, and people who know the suspects. They have collected physical evidence (hair samples, fibre samples, etc.) from the crime scene. They have collected these clues, but have not been able to solve the crime.
They have now asked for your help. Examine the clues, and see if you can solve the crime.
The suspect who owns a purple car was wearing tan shoes. The suspect who weighs 180 pounds owns a green car. The suspect who owns a black car was wearing blue shoes. The suspect who weighs 150 pounds was wearing tan shoes. Brian Martin owns a green car. Marty Jones was carrying a purple umbrella. John Fox has red hair. Larry Smith weighs 210 pounds. The suspect who weighs 190 pounds was wearing blue shoes. The suspect who was carrying a red umbrella is not the one who was wearing black shoes. The thief owns a black car. The suspect who owns a white car is not the one who weighs 170 pounds. Bill Edison was wearing brown shoes. The suspect who weighs 190 pounds is not the one who has red hair.
No two suspects have the same weight, colour shoes, colour umbrella, colour car, or hair colour.
So, the thief owns a black car, was wearing blue shoes, weighs 190 pounds, and doesn't have red hair.
We can eliminate five of the people in the room:
Fred Albert, the victim.
Larry Smith, by (8) weighs 210 pounds.
Brian Martin, by (5) owns a green car.
Bill Edison, by (13) was wearing brown shoes.
John Fox, by (7) has red hair.
Therefore, the only possible thief is Marty Jones.
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Puzzle 2
In this puzzle, all of the numbers from 1 to 8 are used.
The differences (larger − smaller) between any two connected numbers are all different.
Can you complete the grid?
Note: this puzzle is not interactive, and cannot be clicked.
Hint
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist. Start by looking where can the 8 go.
Answer
Reasoning
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist: 1, 2, 3, 4, 5, 6, 7, and let's call these D1, …, D7.
D7 can only happen when: 1 is next to 8 = D7
D6 can happen when:
1 is next to 7, but these are given numbers that are not next to each other. 2 is next to 8 = D6
Where can 8 go? If we put 8 above 1, we cannot also satisfy D6 (2 is next to 8).
Therefore, we have two possibilities:
(a) 8 to the left of 1
(b) 8 to the right of 1 (a) 8 to the left of 1
By D6, 2 would be below 8, and this would give us D1, D6, D7. What can we place to the right of 1?
Not 3, because the difference between 1 and 3, and the difference between 3 and 5, are both D2.
Not 4, because the difference between 4 and 5 is D1, which we would already have.
Not 6, because the difference between 5 and 6 is D1, which we would already have.
There are no possible numbers we can place to the right of 1, so 8 can't go to the left of 1. (b) 8 to the right of 1
By D6, 2 would be above 8, and this would give us D3, D6, D7.
4 can't go next to 1, otherwise we'd create another D3. Therefore, 4 goes in the bottom left corner.
We are now left with 3 and 6.
If 6 went above 4, and 3 above 1, these would both be D2.
Therefore, 3 goes above 4, 6 goes above 1.
The final answer is:
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Puzzle 3
Recently Kevin had a party and because it was his birthday he wanted a mathematical cake!
He ordered a cake in the shape of a cube and had it completely iced (but of course the shop didn't ice the underneath because that just isn't very sensible).
He cut every side of the cake into three equal pieces, giving 27 slices of cake.
He ended up eating all of the pieces of cake that had exactly 2 sides with icing.
So, how many pieces did that leave for the guests?
There are two alternate series, starting with the first two numbers, and each formed by doubling the preceding number in its own series and subtracting 2.
