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Puzzle 197
Three teachers were discussing how long they had each been teaching.
Alex and Billie had been teaching for a combined total of 36 years. Charlie and Billie had been teaching for a combined total of 22 years. Charlie and Alex had been teaching for a combined 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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Puzzle 198
I am a 10-letter word.
My 9, 6, 1, 2 is something a swimmer might do.
My 5, 4, 4, 3 is not that hot really.
My 7, 4, 3, 2 is a long piece of wood.
My 7, 6, 8, 5, 10 is a small part of something.
My 3, 4, 1, 10 is a deep affection.
My 7, 6, 8 is something you can eat.
My whole is an old form of transport.
This is a classic paradox, attributed to Zeno of Elea, a Greek philosopher from Italy. Great minds over the centuries have pondered this paradox, and the scope of a solution is beyond the space available here. It is not even clear that a solution to the paradox actually exists.
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
