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?
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
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Posted by Charlie
on 2020-10-26 15:25:56 |
The values
