BrainBashers™ is a collection of brain teasers & Japanese-type puzzles, optical illusions, and other fun stuff.
BrainBashers has items such as: Daily BB Words, logic puzzles, Sudoku, stereograms, magic games, memory games, mazes, typing tests, and so much more. Including a pointless box and a (nearly) blank page!
puzzles
illusions
fun stuff
There is a wide range of things to do every single day. Take a look at the site map to see a list of everything, or perhaps choose a random page instead.
Daily Puzzle – Jul 02
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
workings
hint
answer
print
www.brainbashers.com
/puzzle/zkld
share
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.
All daily items change at midnight GMT. set time zone
New And Updated Stuff
These items were new / updated in the last 14 days. I also have a more complete list of new / updated items.
Brain TeasersUPDATED – LAST 14 DAYS
New / updated brain teasers twice a month.
