The Birthday Cake Conundrum
Alex has a birthday party, and he's invited 8 of his friends to attend. Seven of them have accepted and showed up. They are about to cut the cake (markings on the cake's perimeter have already been made) when the 8th friend, who is also his best friend, shows up too. Can they still cut the cake into nine equal pieces so that it's mathematically fair (i.e., everyone gets the same amount of cake)? How could they implement the (mathematical) solution in practice? Hint: not all nine pieces need to be of the same shape. Also, you can assume that the cake is a disc where all the material is distributed evenly.
One of Alex's friends came up with a solution to this conundrum. This solution helped Alex realize how to tackle a problem in his Math homework. Based on all this, can you answer the bonus question: which one of the following would be an appropriate gift for Alex: a bicycle with training wheels, a normal bicycle, or a motorcycle? You can assume that Alex is a normal person in terms of his mental and physical development and that none of the people in his party is a mathematical genius!
This simple problem is one I came up with recently, as I was exploring recreational math, particularly Geometry. It can be solved without any advanced tools or methods (in fact, if you employ a bit of imagination, you could solve it in your head, with mathematical precision). Note that this problem would not work if he had a different number of people to divide the cake into (e.g., 7 or 13). There's just something special about the number nine, making the problem lend itself to an elegant geometrical solution. Cheers!
PS - I plan to reveal the solution within a week or so.
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Commenti
Zacharias ๐ Voulgaris
3 anni fa #16
That's actually a slicker approach. Thanks for pointing it out!
Lada ๐ก Prkic
3 anni fa #15
Zacharias ๐ Voulgaris
3 anni fa #14
Zacharias ๐ Voulgaris
3 anni fa #13
Zacharias ๐ Voulgaris
3 anni fa #12
That's the solution I came up with myself! Thank you for your contribution! :-) Just this morning I was talking with a mentee of mine and he came up with another solution, one that's equally elegant. Can anyone guess it?
Lada ๐ก Prkic
3 anni fa #11
Zacharias ๐ Voulgaris
3 anni fa #10
That's one way of doing this! What if we don't have a way to measure angles though? Please don't eat all the cake by yourself - with the lockdown and all, it's hard to find a doctor if you have digestion problems afterwards :-)
John Rylance
3 anni fa #9
John Rylance
3 anni fa #8
Zacharias ๐ Voulgaris
3 anni fa #7
Well, people's imagination may run wild, imagining some weird, uneven cake, so I wanted to make it clear that this is an ordinary birthday cake, like the one in the image I found on Pixabay :-)
Joyce ๐ Bowen Brand Ambassador @ beBee
3 anni fa #6
Debasish Majumder
3 anni fa #5
Zacharias ๐ Voulgaris
3 anni fa #4
, from 3 onwards is when numbers get interesting! :-) Thank you for the share, by the way.
Pascal Derrien
3 anni fa #3
Zacharias ๐ Voulgaris
3 anni fa #2
Randall Burns
3 anni fa #1