Mystery at the Arcade

Question

7 people, A-G, were competing in the national championships of the new arcade game Corpse Deems Us. They each scored a whole number of points from 1 to 100 inclusive, but it wasn't clear what the exact scores were because of the game's weird mechanics. The game gave a logic puzzle so the player had to figure out their exact score.

This time, the game gave every player one clue. The clues were to be used to determine the exact score of every player. The clues are listed by the player who got them.

A) If a player's name is a vowel, their score is a prime number. If a player's name is a consonant, their score is a composite number.

B) The smallest prime factor of your score is 7, and your score is greater than 10.

C) You and one other person scored a square number, and the square roots of them are 2 apart.

D) You scored either 24, 26, 28, or 30 points more than B.

E) Your score is A's score reversed, minus 1. Your score is in between 70 and D's score.

F) Your score is the only score divisible by 5.

G) The greatest score is divisible by 19. You scored in between A and B.

The players could figure out what everyone's score was, and who won the championship. Can you?

Bonus points for figuring out the game's name's relevance to the puzzle.

Answer 1

Scores and winner:

A: 47, B: 49, C: 81, D: 77, E: 73, F:95, G: 48
Making F the winner.

Explanation:

Starting with B the only possible numbers that have 7 as its smallest prime factor (and between 1 & 100) are 49, 77 & 91. From D's clue we find out it is B + another number. If B were 91 or 77 if you add the smallest option (24) to it D's score would be too high so that cancels out those options, making B:49. Since B's score is a square it must be the only other square with C making C have to be the square of 5 or 9 (25 or 81), but since F is the only score divisible by 5 C:81. Also since B is 49, D cannot be B+30 or B+24 or else it would be a prime number and it cannot be B+26 or it would be divisible by 5, making it B+26 so D:77. For E the only prime numbers between 70 and 77 are 71 or 73, but if E were 71 it would make A 27 which isn't prime so E:73 and A:47. Since A:47 and B:49 and G is between them G:48. Finally, F has to be the largest one that is divisible by 19 because the largest of all the others is not divisible by 19. This makes F:95 proving F is the winner.

Answer 2

A) Is a prime.

B) Score is less than 100, but is a multiple of 7 and at least one prime greater than 7.

The only possible scores are 7 * 7 = 49, 7 * 11 = 77 and 7 * 13 = 91.

C) Is a square. One other person is also a square.

D) Score is B + 24, 26, 28, or 30.

B's score must be less than 100 - 24 = 76, so B's score is 49. D's score is 73, 75, 77, or 79. D's score is composite, so D must be 75 or 77, but from F's clue, D is not divisible by 5, so D's score is 77.

E) Is a prime, and A's score reversed minus 1.

So A's score starts with an even number. E's score is between 70 and 77. Primes between 70 and 77 are 71 and 73; add one and reverse to get 27 and 47, of which only 47 is prime and A's score. E's score is 73.

F) Is divisible by 5.

G) The greatest score is divisible by 19.

This is not A or B or D or E or C (square) or G, so must be F. F's score is 5 * 19 = 95.

We still need another square.

B is 7 squared, so C must be 5 squared = 25 or 9 squared = 81. But C is not divisible by 5, so C is 81.

G's score is between A and B.

A is 47 and B is 49, so G is 48.

So the winner is

F, with 95 points.

And the full score list:

F: 95
C: 81
D: 77
E: 73
B: 49
G: 48
A: 47