During the latest round of the BrainBashers school triathlon the final results were mislaid, however, this is what we do know.
Hayden was fourth. Alex was not the oldest but was older than Drew, who was not second. The child who was next in age to the youngest, finished second. The child who finished in third place was older than the child who finished first. Billie was younger than the child who finished in third place.
Can you determine who finished where and place the children in order of age?
Answer # Name Age
#1 Drew youngest
#2 Billie next to youngest
#3 Alex next to oldest
#4 Hayden oldest
Reasoning
By (2), neither Alex nor Drew were the oldest. By (5), neither was Billie. Therefore, Hayden was the oldest, and by (1) came fourth.
#1
#2
#3
#4 Hayden oldest
By (4) the youngest didn't come third, and by (3) the youngest didn't come second. Therefore, the youngest came first.
#1 youngest
#2
#3
#4 Hayden oldest
By (3), the next to youngest came second, leaving the next to oldest in third.
#1 youngest
#2 next to youngest
#3 next to oldest
#4 Hayden oldest
By (2), Drew wasn't second, but Alex was older, so Drew can't be third either. Therefore, Drew can only have come in first.
#1 Drew youngest
#2 next to youngest
#3 next to oldest
#4 Hayden oldest
By (5) Billie didn't come third, so came second. Leaving Alex in third.
#1 Drew youngest
#2 Billie next to youngest
#3 Alex next to oldest
#4 Hayden oldest
??
Puzzle 3
During the recent BrainBashers Football Competition, 5 teams were competing.
Each team played each other just once, with 2 points for a win, 1 point for a draw, and 0 points for a loss.
However, the rain damaged the final scoresheet, and this is all that could be read of the final points after all of the matches:
Rugby 6
Grimsby 5
Hereford 4
Lichfield 2
Reading ?
Can you work out how many points Reading ended the season with?
Reasoning
There were 5 teams in the league, and every team played every other, so there were a total of 10 games played:
Rugby vs Grimsby
Rugby vs Hereford
Rugby vs Lichfield
Rugby vs Reading
Grimsby vs Hereford
Grimsby vs Lichfield
Grimsby vs Reading
Hereford vs Lichfield
Hereford vs Reading
Lichfield vs Reading
We know that 2 points were allocated for each game played. Which means that there were a total of 20 points over the 10 games.
Since the given results add to 17, the remaining 3 points belong to Reading.
Here is a snippet of section A of the curious multiple-choice entrance exam into the exclusive BrainBashers puzzle club.
Q1. The first question with B as the correct answer is:
A. Q1
B. Q4
C. Q3
D. Q2
Q2. The answer to Q4 is:
A. D
B. A
C. B
D. C
Q3. The answer to Q1 is:
A. D
B. C
C. B
D. A
Q4. The number of questions that have D as the correct answer is:
A. 3
B. 2
C. 1
D. 0
Q5. The number of questions that have B as the correct answer is:
Answers
Q1. C (the first question with B as the correct answer is Q3)
Q2. D (the answer to Question 4 is C)
Q3. B (the answer to Question 1 is C)
Q4. C (the number of questions that have D as the correct answer is one)
Q5. B (the number of questions that have B as the correct answer is two)
Reasoning
A complicated, and sometimes, confusing answer!
Can Q1 be A? No, because this would tell us that Q1 was the first question with B as the answer, which would be a contradiction (as we've just assumed Q1 was A).
Can Q1 be B? No, because this would tell us that Q4 was the first question with B as the answer, which would be a contradiction (as we've just assumed it was Q1).
Can Q1 be C? Possibly, because Q3 points back to Q1 correctly, and is logically consistent.
Can Q1 be D? No, because:
Q2 would be B Q4 would be A, which means that we have three questions with D which means that Q3 would have to be D, and this would tell us that Q1 is A, which would be a contradiction (as we've just assumed that Q1 is D).
Therefore, Q1 is C, which means that Q3 is B.
We can ignore Q2 for a moment, as it asks us about Q4, and look at Q4 first.
Looking at Q4 (how many questions have D as the answer) it can't be D (zero), as this would contradict itself.
It can't be A (three) as we only have two other questions without an answer.
If Q4 was B, then the remaining questions (Q2 and Q5) would both have to be D, and:
Q5 being D would mean that only one question was B, which would be a contradiction (as Q3 is already B, and we've just assumed that Q4 is also B).
So Q4 must be C, which means that Q2 is D.
Looking at Q5, it can't be A (as Q3 is B), it can't be D (as Q4 tells us that we only have one question with D as the answer, Q2). It can't be C as we don't have three questions that are B. So Q5 is B (the two questions are Q3 and Q5).
