Apr 9th, 2007
Brain Teaser: Party For Polyglots & Introducing Wes Carroll, Puzzle Master
We are delighted to introduce you to Wes Carroll who has graciously created a few new puzzles to bend all those sharp brains out there! Keep checking back, as we will continue to release new puzzles regularly.
Wes aspires to the Renaissance ideal of excellence in multiple fields: he is the head of Do The Math private tutoring services, Puzzle Master for the Ask A Scientist lecture series, and an internationally touring performer and teacher of music. Find out more at wescarroll.com.
With no further ado, the first puzzle!
Party For Polyglots
Difficulty: MEDIUM
Type: LOGIC
Question:
Of the 100 people at a recent party, 90 spoke Spanish, 80 spoke Italian, and 75 spoke Mandarin. At least how many spoke all three languages?
Have you solved it yet? If you are working the problem, making hypotheses, testing your ideas, and coming up with a solution, you are using your frontal lobes. This is great exercise because the frontal lobes follow the "last hired, first fired" adage. They are they last areas of your brain to develop and the first to suffer the ravages of time and stress. So, keep exercising! Just like your voluntary muscles, regular brain workouts will help you keep more active neuronal circuits in your brain which helps you function better today, as well as create a protective barrier against aging.
Click to read the answer.
Let us know what you think of the puzzle and please welcome Wes!
[...] Many of this weeks submissions presented problems, of varying difficulty. As a warm-up, Sharp Brains' new puzzle master offers a brainteaser entitled 'Party For Polyglots'. More demanding are two entries from MathNotations, aimed at calculus students: the first concerning properties of the ellipse, the second, more advanced post is on exploring infinite series. We close with the most amibitious material, the Unapolagetic Mathematician's examination of the knot colouring problem: for the background, see here; this week's submission explains what's going on. I feel that I had an unfair advantage since my flatmate is a knot-theorist; I'm often intrigued by the techniques applied to this field. Plus I rarely get to draw pictures during my own research! [...]
If you liked this puzzle, you can try a few more by other puzzlers at The Carnival of Mathematics. Enjoy!
[...] Party For Polyglots A brain teaser puzzle, not too difficult. [...]
I like it. I actually solved it from the opposite direction: I started with the speakers of one language and subtracted.
Glad you liked it, and creative solutions are always encouraged!
[...] 35. Join this Party For Polyglots. [...]
At least ONE person can speak all three languages.
Used same method as The Science Pundit.
Population = 100
Within the population,
Spanish Speakers = 90
Italian Speakers = 80
Mandarin Speakers = 75
So, for the minimum number of all three language speakers or total overlap...
x = 90 - (100 - 80) - (100 - 75)
9/10 x 8/10 x 3/4 = 216/400 => 54 People
90+80+75=245 language/people
245-200=45
there were 45 more language/people than if 2 languages were spoken by all 100 people.
I challenge someone to create a Venn diagram with 45 people for 3 languages and have the various totals add up correctly