The 50 Cent Riddle That Stumped Australian Students



A 50 cent coin has 12 equal sides. If you place two coins next to each other on a table (see video for diagram), what is the angle formed between the two coins?

This was asked to 12th grade (age 17 and 18) students in Australia. Many were confused and the math problem went viral after they took their frustration to social media.

Can you figure it out? The video presents two methods to solve this problem.

The first solution is an example of a semiregular tessellation (thanks to Mathologer for pointing this out)
http://mathworld.wolfram.com/SemiregularTessellation.html

Coverage in the media
http://www.theage.com.au/victoria/vce-maths-problem-can-you-solve-the-50-cent-question-20151102-gkopm8.html

http://home.bt.com/news/world-news/can-you-work-it-out-maths-students-stumped-by-50-cent-piece-poser-but-teachers-claim-it-was-too-easy-11364014231519

Thanks to Mathologer for informing me of this puzzle. I referenced his video “Math is Illuminati confirmed” in the video. Check out the video and do subscribe to Mathologer: https://www.youtube.com/watch?v=DfnBW6HvNwM

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31 thoughts on “The 50 Cent Riddle That Stumped Australian Students

  • September 29, 2017 at 4:26 pm
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    Solved by understanding we are dealing with half of 360 degrees which 180.
    3x=180
    X= 180/3
    X= 60

    Reply
  • September 29, 2017 at 4:26 pm
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    1:06 i noticed that you could do that in 0:58

    after the video, i noticed that my method is a bit similar to yours. its just that i used internal angles..

    Reply
  • September 29, 2017 at 4:26 pm
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    i tried it on some equations i made… or… discovered.. whatever i just came up with it k

    so 12 sides…

    180-(360/12)
    180-30
    150.

    (360-2(150))/2
    (360 – 300)/2
    60/2
    30

    ok now imma watch the vid

    oh lemme change the equation since i saw how they were placed.

    360-2(150)
    360-300
    60

    ok lemme check if this is correct

    Reply
  • September 29, 2017 at 4:26 pm
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    Solved it in a couple of seconds. Draw two isoceles triangles back to back, the angles measures are 30-75-75 degrees for each triangle. Draw a horizontal lines and measure the angle that is created by the triangle and this horizontal to be 15 degrees. Draw another isoceles triangle next to (or rather below) one of the two that you drew (so your essentially drawing the next piece of the 12 sided polygon). You subtract the 15 degrees from the 75 degrees of the triangle drawn below because only 60 degrees of the third triangle you drew is below the horizontal. The two sides are symmetrical. So 60+60=120. Subtract this from 180 and you have 60 degrees. Its better if I could draw it, but I can't here.

    Reply
  • September 29, 2017 at 4:26 pm
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    Australian education doesn't do much to keep the stragglers up to speed in maths. Plenty of Aussie kids would get this in a second, but, yeah, a lot would have been stumped.

    Reply
  • September 29, 2017 at 4:26 pm
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    Welp, I did this a third way.

    180(12-2) = 1800 (Sum of all angles inside the coin)

    1800/12 = 150 (One angle of the coin)

    Since angles at a point add up to 360, 360 – 2×150=360-300=60

    Reply
  • September 29, 2017 at 4:26 pm
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    Strictly speaking, we are not given enough information to solve this problem. We are merely told that the coin has 12 equal sides, not that it is a regular polygon. 🙂

    Reply
  • September 29, 2017 at 4:26 pm
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    There are two answers 30 degrees and 60 degrees. When two sides are in contact it is 60 degrees and when two edges are in contact then it is 30 degrees. It is a multiple answer question. Besides if the edges are in contact in an irregular way then there will be two answers for that as well ranging from 0-60. I hope you get it.

    Reply
  • September 29, 2017 at 4:26 pm
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    It is not specifically mentioned whether the sides or the edges are in contact.

    Reply
  • September 29, 2017 at 4:26 pm
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    There are two answers 30 degrees and 60 degrees. When two sides are in contact it is 60 degrees and when two edges are in contact then it is 30 degrees. It is a multiple answer question.

    Reply
  • September 29, 2017 at 4:26 pm
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    I figured it out by figuring out the interior angle (the sum of measures of interior angles is (n-2)*180, where n is the number of sides. so the sum of the angles is 1800. Then I divided by 12, since it is a regular 12-gon. This gives us each interior angle is 150 degrees.). Then the exterior angle is 180-150=30. So by the same logic as your video, theta is 60 degrees.

    Reply
  • September 29, 2017 at 4:26 pm
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    I went the long way around…

    Sum of angles on the inside being 1800, (180 in a triangle, 360 in a square, 540 in a pentagon and so forth)

    Divided by number of angles – 1800/12=150

    Got the outside angle by Subtracting 150 from 180 = 30

    Took that times two since it's two coins side to side, doubling the outside angle – 30*2=60.

    I see now how it took way longer than it should have…

    But hey.. 🙂

    Reply
  • September 29, 2017 at 4:26 pm
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    Got it. Through something similar to #2. The bottom angles of the empty spot between coins add up to equal our angle.
    🙂
    If you continue our angle's lines down to table they'll form an inner triangle (a), and each an outside triangle triagle (b1, b2) with the lower sides of the coins…

    A side's ends angles are equal, and they too add up to equal our angle. That means the 3rd angle of (b) equals the two angles formed on the table by (a). So… the a side coming from our angle splits the table in a 2/3 angle of 180", and into a 1/3 one.

    … therefore… the bottom angles of triangle (a) are 60" and 60"… so our angle is 60" as well.

    Reply
  • September 29, 2017 at 4:26 pm
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    I did this in about 20 seconds and I'm sure many others did too, lol.

    Reply
  • September 29, 2017 at 4:26 pm
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    This was probably just a question on a foundation maths supported learning group, not a maths B or C question

    Reply
  • September 29, 2017 at 4:26 pm
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    well those guys failed math if I (a 12 year old) can work it out in a few secs. Seems Australia need to re-evaluate their way to teach.

    Reply

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