Reasoning
703 can only be broken down into 19 x 37, it has no other factors.
??
Puzzle 131
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.
?
Puzzle 132
Three teachers were discussing how long they had been teaching.
Alex and Billie had been teaching for a total of 36 years. Charlie and Billie had been teaching for a total of 22 years. Charlie and Alex had been teaching for a total of 28 years.
How long had each been teaching?
Hint
If we look at all of the clues, each person appears exactly twice.
Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.
Reasoning
If we look at all of the clues, each person appears exactly twice.
So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.
So, Alex + Billie + Charlie = 43 years.
In each clue we are given two of the people, so we can use this to find the missing person:
Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 – 22 = 21 years.
Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 – 28 = 15 years.
Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 – 36 = 7 years.
Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:
[1] A + B = 36 [2] C + B = 22 [3] C + A = 28
If we use [3] – [2] we have:
[4] A – B = 6
If we use [1] + [4] we have:
2A = 42 A = 21
By [1] B = 15. By [3] C = 7.
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