Sharp Brains: Brain Fitness and Cognitive Health News

Neuroplasticity, Brain Fitness and Cognitive Health News


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! Wes Carroll

Wes 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. With no fur­ther ado, the first puzzle!

Party For Polyglots

Dif­fi­culty: MEDIUM

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.


10 could not speak Span­ish, 20 could not speak Ital­ian, and 25 could not speak Man­darin. So there could have been 10 peo­ple who spoke none of those languages.

How­ever, that would max­i­mize the num­ber of peo­ple who could speak all three, and the prob­lem asks at least how many speak all three. There­fore, we must assume that these 10, 20, and 25 peo­ple are all sep­a­rate peo­ple. Hav­ing iden­ti­fied 55 each of whom is miss­ing one lan­guage, the remain­ing 45 speak all three.


PS: Enjoy these 50 brain teasers to test your cog­ni­tive abil­ity. Free, and fun for adults of any age!

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17 Responses

  1. […] 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! […]

  2. Caroline says:

    If you liked this puz­zle, you can try a few more by other puz­zlers at The Car­ni­val of Math­e­mat­ics. Enjoy!

  3. […] Party For Poly­glots A brain teaser puz­zle, not too difficult. […]

  4. I like it. I actu­ally solved it from the oppo­site direc­tion: I started with the speak­ers of one lan­guage and subtracted.

  5. Caroline says:

    Glad you liked it, and cre­ative solu­tions are always encouraged!

  6. pjsk8 says:

    At least ONE per­son can speak all three languages.

  7. Beck says:

    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)

  8. k says:

    9/10 x 8/10 x 3/4 = 216/400 => 54 People

  9. scott says:

    90+80+75=245 language/people


    there were 45 more language/people than if 2 lan­guages were spo­ken by all 100 people.

  10. BJ says:

    I chal­lenge some­one to cre­ate a Venn dia­gram with 45 peo­ple for 3 lan­guages and have the var­i­ous totals add up correctly

  11. Eric says:

    For the Venn dia­gram: 25 speak Ital­ian and Span­ish, 20 speak
    Man­darin and Span­ish, and 10 speak Man­darin and Italian.

  12. allstar says:

    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

  13. ddd69 says:

    10 cant speak span­ish
    20 cant speak ital­ian
    25 cant speak man­darin
    100 — (10+20+25)= 45
    can speak 3 languages

  14. michelle says:

    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.

  15. Abhishek says:

    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

  16. abhishek says:

    prob­lem can be solved by two method…the log­i­cal way give us 45..but per­son who do lat­eral think­ing kind of puz­zle must reply 1..

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