Sharp Brains: Brain Fitness and Cognitive Health News

Neuroplasticity, Brain Fitness and Cognitive Health News


#14 Brain Teaser: Party For Polyglots

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 them!


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.

Next brain teas­er in Sharp­Brains’ top 25 series:

Leave a Reply...

Loading Facebook Comments ...

19 Responses

  1. Caroline says:

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

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

  3. Caroline says:

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

  4. pjsk8 says:

    At least ONE per­son can speak all three lan­guages.

  5. 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)

  6. k says:

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

  7. scott says:

    90+80+75=245 language/people


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

  8. BJ says:

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

  9. Eric says:

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

  10. 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

  11. ddd69 says:

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

  12. 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.

  13. 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

  14. 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..

  15. Brad Donner says:

    A min­i­mum of ten could not speak all three lan­guages; and a max­i­mum of 75 could, all con­sid­ered with­out assump­tions.

  16. Brad Donner says:

    I stand cor­rect­ed. A min­i­mum of 25 could not speak all three, and a max­i­mum of 75 could; allow­ing that some only speak one or two lan­guages.

  17. Javier says:

    i have a ques­tion about this rid­dle.
    the rid­dle is pro­posed as if there are exact­ly 100 of peo­ple at the par­ty.
    So, if you think so, this prob­lem maybe be equal to a prob­a­bil­i­ty prob­lem to find the num­ber of pos­si­bil­i­ties to find a per­son between 100 who speaks Span­ish, Ital­ian and Chi­nese lan­guage. If you applies prob­a­bil­i­ty the­o­ry to find event P(S ? I ? M) (S: Span­ish) (I: Ital­ian) (M: Man­darin) of a per­son that speaks these lan­guages. So, if you mul­tip­plies the prob­a­bil­i­ties of speak Span­ish, Ital­ian and Man­darin the answer is 54.
    I imag­ine that there was a mis­take of my part but if some­one could help me, I will thank very much.

Leave a Reply

Categories: Brain Teasers

Tags: , , , , , , , , , , ,

Watch All Recordings Now (40+ Speakers, 12+ Hours)

About SharpBrains

As seen in The New York Times, The Wall Street Journal, BBC News, CNN, Reuters and more, SharpBrains is an independent market research firm tracking health and performance applications of brain science.

Follow us and Engage via…

RSS Feed

Search for anything brain-related in our article archives