# The Game of Differences - Colegiul Național din Iași (Iași - Roumanie)

Titre du sujet:
The Game of Differences
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Résumé:
Research topic: There are 4 natural numbers a, b, c, d written on a row. The differences |a-b|, |b-c|, |c-d|, |d-a| are then written on the next row. The process is continued: 7 3 9 2 4 6 7 5 2 1 2 1 1 1 1 1 0 0 0 0 It can be observed that the null row 0, 0, 0, 0 has been obtained.  Is this a coincidence or is the null row obtained for any natural numbers a, b, c, d?  What happens if the rows don’t have 4 numbers, but 3, 5, 6,...?  What happens if we have 4 rational numbers  What happens if we have 4 real numbers Brief presentation: • We solved the natural numbers’ case using remainders modulo 2. • We also treated the cases of 3, 4, 5, 6, 7, 8, … natural numbers on the first row, obtaining different conclusions, afterwards we made a C++ program. • We extended the case of integers, followed by rational numbers. • Subsequently, we prove significant results for real numbers.
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Nombre d'élèves :
7