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MathNet 2017-part-02 — 176 problems (EN–VI) Question 17

Math Olympiad Vault · MathNet 2017-part-02 — 176 problems (EN–VI)

Question 17

Gargamel caught $N$ Smurfs and distributed them into three bags. After moving Papa Smurf from the first bag to the second, Grouchy Smurf from the second bag to the third, and Smurfette from the third bag to the first one, the average Smurfs' height in the first bag decreased by 8 millimetres, while the average Smurfs' heights in the second and the third bag increased by 5 and 8 millimetres, respectively.
If there were nine Smurfs in the first bag, determine $N$. (Stipe Vidak)