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Money giveaway (Posted on 2020-10-26) Difficulty: 3 of 5
Eve and Martti have a whole number of euros.

Martti said to Eve: "If you give me three euros, so I have n times the money compared to you."
Eve in turn said to Martti: "If you give me n euros then I have triple the amount of money compared to you".

Suppose, that both claims are valid. What values can a positive integer n get?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution The values | Comment 2 of 5 |
m + 3 = n * (e - 3)

e + n = 3*(m-n)

e = 3m - 4n

m + 3 = 3mn - 4n^2 - 3n

(1-3n) m = -3 - 4n^2 - 3n

Solving for m, then e, in terms of n:
     n     m     e
     0    -3    -9  Assuming negative value, n=0 is invalid.
     
The valid solutions:
     
     n     m     e
     1     5    11
     2     5     7
     3     6     6
     7    11     5
     
Higher values of n seem to have e approach 4.333... asymptotically.     
     

for n=0:100000
   m=(3+4*n^2+3*n)/(3*n-1);
   e=3*m-4*n;
   if m==floor(m)&&e==floor(e)
      disp([n,m,e])
   end
end


Edited on October 26, 2020, 10:52 pm
  Posted by Charlie on 2020-10-26 15:25:56

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