Pretty Pencils

Number Theory Level 3

If the total number of pencils above equals x y y x x^{y}y^{x} , where x , y x, y are prime numbers, calculate x + y x + y .


The answer is 5.

Tom Engelsman by tom engelsman , 45, USA

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2 solutions

Tom Engelsman
Oct 30, 2017

The above pencil sculpture consists of four interlocking hexagonal arrays (each having 18 pencils). Thus, the total number of pencils = 72 = 2 3 3 2 72 = 2^{3}3^{2} and x + y = 2 + 3 = 5 . x + y = 2 + 3 = \boxed{5}.

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Nice solution.

Hana Wehbi - 3 years, 7 months ago

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Thanks, Hana.......of course, the above pencil artist probably cheated with crazy glue!!

tom engelsman - 3 years, 7 months ago

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Yeah, but I really like how you stated the problem.

Hana Wehbi - 3 years, 7 months ago

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@Hana Wehbi – Yup, it's simple & elegant :)

tom engelsman - 3 years, 7 months ago

Elegant and concise solution to a nice problem.

Thomas Sutcliffe - 3 years, 7 months ago

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Thanks, Thomas!

tom engelsman - 3 years, 6 months ago
Venkatachalam J
Apr 1, 2019

The total number of pencils:

Horizontal(18)+Vertical(18)+Diagonly(18+18)=72= 2 3 3 2 2^{3} 3^{2}

Hence the required solution is 2+3=5

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