Darts

Number Theory Level 2

You can throw an unlimited number of darts at this dartboard.

Some total scores are impossible to obtain such as all numbers less than 5 as well as 6,8 and 9. What is the highest whole number score that is impossible to obtain?

31 18 23 29

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Bobbym None
Sep 20, 2014

You can always compute the Frobenius number when n = 2 by using Sylvester's formula. (5*7) - 5 - 7 = 23

4 Helpful 0 Interesting 0 Brilliant 0 Confused

This is called a Frobenius Number.

I do not have a constructive algorithm to get that frobenius(5,7) is 23. However, I have a proof that 23 indeed is the required number.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The Frobenius number of ( a , b ) (a,b) is a b − a − b ab-a-b .

Satvik Golechha - 6 years, 8 months ago

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yup, see bobbym's solution

Agnishom Chattopadhyay - 6 years, 8 months ago

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