Maths Trick To Fool Your Friends

A little maths problem I posted on my blog became one of my most popular posts, and still draws traffic daily from Google.

Here’s something for you guys to try out at home – don’t worry, there’s nothing difficult, only adding and subtracting, but make sure the difference between the 1st and 3rd digits is at least 2 in your number.

Do let me know the number you chose and the answer you got.


45 thoughts on “Maths Trick To Fool Your Friends

      1. Presumably, “+” here means some binary operator other than addition. There are infinitely many binary operators that satisfy the two equations, giving infinitely many solutions. One of those binary operations is the sum of a multiple of two unknowns. We can therefore find one possible answer to the silly question by solving:

        If 2x+5y=16 and 6+8=7, what is 6x+2y.


        2x + 5y = 16

        6x + 8y = 7

        6x + 15y = 48

        7y = 41

        y = 41/7 = 82/14

        2x + 205/7 = 16

        2x = 16 – 205/7

        x = 8 – 205/14 = (8 * 14 – 205) / 14 = (112 – 205)/14 = -93/14

        6x = -558 / 14

        2y = 164 / 14

        6x + 2y = -394 / 14 = -198 / 7

        This gives the unwieldy answer -198/7.

        This is probably not the answer Chris hoped for. He ought, therefore, to ask his questions more carefully.

  1. The number first thought of is 100a + 10b + c, for some (a,b,c) where {a,b,c} is a subset of {0,1,2,3,4,5,6,7,8,9}. It’s reverse is 100c + 10b + a. The difference is 99 x |(a – c)|.

    The difference is therefore 99n, where n is a member of of {2, 3, 4, 5, 6, 7, 8, 9,}.

    In H~T~U notation (hundreds, tens and units), 99n is (n-1)~9~(10-n) for all eight possible values of n, and its reverse is (10-n)~9~(n-1), which also happens to equal 99 x (11-n). For example, if n is 3, then 99n is 297,and its reverse is 99 x 8, which is 792.

    (n-1)~9~(10-n) + (10-n)~9~(n-1) = 900 + 180 + 9 = 1,089 Q.E.D.

  2. Reblogged this on and commented:
    One of my ex-boyfriends a loong time ago was quite a math wizard. My math knowledge is at the 3rd grade level which is why I should probably start relearning with my daughter who is 9. I’ll save this here for any of you who get a kick out of it (and for myself for future study!).

    1. Thanks for the reblog – it’s never to late to learn. People tend to put down their maths skills, and a recent report in the UK suggested that parents often put their children off maths by saying how bad they are at it.

  3. Yes, any number chose will result in 1089. But, step 3 is wrong, if you take the large number from the small number (using your example) you end up wit -297, not 297, in which case the rest of the math doesn’t work out. Seen this before, still fun.

      1. 965.

        Neat trick, by the way. The answer’s always the same no matter what number is used (as long as it follows the rules).

      2. First: any three-digit number where the 1st and 3rd digits are 1 apart gives 99 upon subtraction of its opposite. Any three digit number whose 1st = 3rd obviously gives 0.
        Second: every other three-digit number when subtracted by its opposite always gives a three-digit number that has a 9 as its second digit, whereas its 1st and 3rd digits will always add to give 9. When adding, then, its essentially like adding 999 by 999.
        Aaaaaaaaaaaaaaannnnnnnnnndddd there you go!

      1. Thanks, I made a small error in the original which has been fixed – you must take the small number from the larger number, so it will be 954 – 459 all the time.

        Apologies – I need someone to proof read before posting this stuff.

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