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 Money giveaway (Posted on 2020-10-26)
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)

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 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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