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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Puzzle 290
Start from the central 'F' and move horizontally or vertically, and collect the letters needed to spell 'FIND' (in any order). How many routes can you take?
D
N
I
D
D
N
D
I
D
D
I
N
F
I
I
N
I
N
D
D
I
D
I
D
N
Note: this puzzle is not interactive, and the letters cannot be clicked.
Reasoning
Starting with the central F, you can move:
Up (D), Up (I), Left (N).
Left (N), Left (I), Left (D).
Left (N), Left (I), Up (D).
Down (D), Left (N), Left (I).
Down (D), Down (I), Down (N).
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Puzzle 291
Apparently, one side of a cat has more hair. The findings of the scientific establishment have been corroborated by a special enquiry by the BB Feline Federation. Many hair counts were taken of the side in question and consistently it was found to contain more hairs. The scientists determined that more hair was required on this side to insulate the cat from the elements while it was lying down. Perhaps you would like to examine a cat to confirm the findings. Before you do, can you guess which side of a cat has more hair?
