Puzzle 57
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?
Puzzle Copyright © Kevin Stone
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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.
Puzzle 58
Which of the shapes is identical to the first one?
There might be more than one.
Puzzle Copyright © Robert A. Hartmann
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Share link: https://www.brainbashers.com/puzzle/zdyr
Hint
Try to rotate them around in your head, but watch out for mirror images.
Puzzle 59
What day would tomorrow be if …
… yesterday was five days before the day after Sunday's tomorrow?
Puzzle Copyright © Kevin Stone
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Share link: https://www.brainbashers.com/puzzle/zyfp
Hint
Try working backwards.
Answer
Saturday.
Reasoning
It's best to work backwards:
"Sunday's tomorrow"
is Monday.
"the day after Sunday's tomorrow"
is therefore Tuesday.
"five days before the day after Sunday's tomorrow"
is therefore Thursday.
"yesterday was five days before the day after Sunday's tomorrow"
yesterday was Thursday, making today Friday. Therefore tomorrow is Saturday.
Puzzle 60
This BrainBashers safe has a rather unusual control panel.
In order to open the safe, you have to press every single square once only, in the correct sequence, ending on the square marked E.
Each square indicates which square to press next, for example, 2U means move up 2 squares and 3R means move right 3 squares.
Can you determine which square you must start with?
| 4R |
4D |
1R |
1D |
2D |
4L |
1D |
| 1R |
4D |
5D |
2R |
2D |
1L |
4L |
| 2R |
1D |
1L |
2R |
2R |
2D |
2U |
| 2R |
2R |
3U |
3D |
1R |
3U |
6L |
| 3U |
3R |
1D |
2U |
4L |
2D |
3L |
| 3U |
1L |
1R |
1R |
1R |
1R |
2U |
| 6U |
E |
2U |
2L |
4L |
1L |
2U |
Note: this puzzle is not interactive, and the safe buttons cannot be clicked.
Puzzle Copyright © Kevin Stone
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Share link: https://www.brainbashers.com/puzzle/zixy
Hint
Start on any square, and see how far you get.
Answer
Start from the 2U in the bottom right-hand corner.
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