ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Some Interesting Math Problems

Updated on August 7, 2018


I am searching through my files finding some good Mathematics materials when I come across these Math Excercises. I choose some interesting problems that are of some topics in Algebra and Probability. I present here the problems with their solutions.

Problem Number One :

An apple, an orange, a banana and a pear are laid out in a straight line . The orange is not at either end and is somewhere to the right of the banana. In how many ways can the fruit be laid out ?

Solution :

The orange (O) must be on the second or third place from the left. The banana (B) must be somewhere to the left of the orange. Hence the placement of the banana and the orange may take any of three forms namely BO_ _ , B_O_, or _ BO_. In each case two ways remain to fill in the open positions with an apple (A) and a pear (P). The total number of ways equals 3*2 or 6. The ways can be listed as follows:


Problem Number Two :

Near the end of a party , everyone shakes hands with everybody else. A straggler arrives and shakes hands with only those people whom the straggler knows . Altogether sixty-eight handshakes occurred. How many other people at the party did the straggler know ?

Solution :

If all n people at a party shake hands with all others present then n (n- 1)/2 handshakes will take place altogether . Hence, the number of handshakes before the straggler’s arrival must have been sixty-six because that is the largest plausible value less than sixty-eigh . The straggler must have known two other people at the party. Constructing a table of possible values of n(n-1/2 clarifies that sixty-six is the only plausible number.

N n(n-1)/2

7 21

8 28

9 36

10 45

11 55

12 66

13 78

Problem Number Three :

Note that 1647/8235 = 1/5, start with 1647/8235, and delete one digit from both the numerator and the denominator to create an equivalent fraction. Then delete another pair to create another equivalent fraction.

Solution :

The successive equivalent fractions are 167/835 and 17/85 . The author Barry R. Clarke notes that this fraction is the only “sequential digital deletion fraction” with four digits in both the numerator and denominator that includes eight different digits.

Problem Number Four :

The supplement of an angle is 78 degrees less than twice the supplement of the complement of the angle . Find the measure of the angle,

Solution :

Let A = be the measure in degrees of the angle.

180 – A = be the supplement of this angle.

90 - A = be the complement of the angle .

Working equation :

(180 - A ) + 78 = 2 ( 180 - (90 – A) )

258 - A = 2 (90 + A )

258 - A = 180 + 2A

78 = 3A

A = 26


    0 of 8192 characters used
    Post Comment

    • profile image


      5 years ago

      I LIKE IT

    • profile image


      5 years ago


    • profile image


      6 years ago

      Really helpful for my mathematical science work

    • profile image

      Mrigank Mongia 

      7 years ago

      Interesting collection :)

    • profile image

      priyanka pokharel 

      7 years ago


    • profile image


      7 years ago

      very nice

    • profile image


      7 years ago

      send me more/////..

    • profile image

      Mayank kejriwal 

      7 years ago

      That was really wonderful...stil looking for more harder qustions

    • profile image


      7 years ago

      those were really good.can you please send me some more in

    • profile image


      8 years ago


    • Shahid Bukhari profile image

      Shahid Bukhari 

      8 years ago from My Awareness in Being.

      I would play the game, if it were not forbidden in my Belief ... Islam.

    • pemekwulu profile image


      8 years ago from USA

      Problem No. 2 sounds like application of triangular numbers. Sounds interesting!

    • jayb23 profile image


      8 years ago from India

      Awesome Maths problems, made me remember my chilhood days.

    • profile image


      8 years ago

      Thank you sooo much cause I had to make my own interesting maths problems and I used yours. My name is not IliveinThailand of course but I'm not going to tell you my real name other wise if my maths teacher saw this and there was my name, he will detension me. Hahahaha! well Thanks again!!!! xxx

    • profile image


      8 years ago

      Thanks for the problems.

      For the handhake problem, it must have been 12 people at the party becaue more than that, and there'd be more than 68 handhakes. If it were 11 people, then that would mean the straggler knew 68-55 = 13 people - but there are only 11, so that's impossible. The same applies for 10 or less people.

    • Coolmon2009 profile image


      9 years ago from Texas, USA

      Interesting hub thanks for sharing

    • profile image


      9 years ago

      It is interesting.Now I want to ask you one:

      Now I have a watermelon ,I just want to cut it 3 times to make it 7 parts;and when I eat all parts ,the corver of it will be 8 parts.Please help me solve this problem.Thanks.

    • profile image


      9 years ago

      really good one,can you write few more please.

    • creation75 profile image


      9 years ago from India

      Very interesting. Want more from you.

    • Research Analyst profile image

      Research Analyst 

      9 years ago

      Math has always been a fascinating thing to me but the part I like most is once you learn the correct formulas, it pretty much is the same across the board, unlike english which is always changing. Math problems really makes us become solution orientated.

    • profile image


      9 years ago


    • profile image


      9 years ago

      thank you

    • priya shetty profile image

      priya shetty 

      9 years ago


    • profile image


      10 years ago

      Thanks for the questions

      Did them all

      Really interesting.

    • profile image


      10 years ago

      i finished all the questions.

      if u have further interesting questions can u send them to my email?

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      11 years ago from Manila

      Your welcome Kenny. God bless you.

    • Kenny Wordsmith profile image

      Ashok Rajagopalan 

      11 years ago from Chennai

      Thank you, though my little mind boggles!


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)