Apr 9, 2007
Brain Teaser: Party For Polyglots & Introducing Wes Carroll, Puzzle Master
By: Caroline Latham
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
For the Venn diagram: 25 speak Italian and Spanish, 20 speak
Mandarin and Spanish, and 10 speak Mandarin and Italian.
i remember doing this exact same question in maths at school. finally got it, took me a while to remember how
10 don’t speak spanish
25 don’t speak mandarin
20 don’t speak italian
therefore the rest speak all languages – 45 … if that makes sense
10 cant speak spanish
20 cant speak italian
25 cant speak mandarin
so
100 – (10+20+25)= 45
can speak 3 languages
pjsk8 is right. I don’t think the writer intended it, but the way the question was phrased, it is asking for the minimum of speakers that can speak all three languages. That being 1.
the work “atleast” is key.
10 peoples cannot speak spanish, 20 people cannot speak Italian and 25 cannot speak mandrin. Adding all of them comes 55. So there are 55 people who cannot speak alteast one language. Remaining 45 people can speak all the three languages. It is logically very good puzzle!!! Thanks for such stuff