Problem K. 874. (November 2025)
K. 874. András, Bori, Cili, Dezső, Elemér, Feri, Gabi and Hugó are standing in a circle in this order, each holding some beans, with a total of 240 beans altogether. If András gives 1 bean each to Bori, Cili, Dezső, Elemér, Feri, Gabi, and Hugó, then Bori gives 2 beans each to Cili, Dezső, Elemér, Feri, Gabi and Hugó, then Cili gives 3 beans each to Dezső, Elemér, Feri, Gabi and Hugó, then Dezső gives 4 beans each to Elemér, Feri, Gabi and Hugó, then Elemér gives 5 beans each to Feri, Gabi, and Hugó, then Feri gives 6 beans each to Gabi and Hugó, then Gabi gives Hugó 7 beans, each of them will have the same number of beans in their hands. How many beans did each of them have initially?
(5 pont)
Deadline expired on December 10, 2025.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle 240:8=30\), így a végén mindenkinél 30 babszem lesz. Hugó összesen \(\displaystyle 1+2+3+4+5+6+7=28\)-at kapott, így nála \(\displaystyle 2\) volt, Gabi összesen \(\displaystyle 1+2+3+4+5+6=21\)-et kapott és \(\displaystyle 7\)-et adott, így nála \(\displaystyle 16\) volt, Feri összesen \(\displaystyle 1+2+3+4+5=15\)-öt kapott és \(\displaystyle 12\)-t adott, így nála \(\displaystyle 27\) volt. Elemér \(\displaystyle 1+2+3+4=10\)-et kapott és \(\displaystyle 15\)-öt adott, így nála \(\displaystyle 35\) volt. Dezső \(\displaystyle 1+2+3=6\)-ot kapott és \(\displaystyle 16\)-ot adott, így nála \(\displaystyle 40\) volt, Cili \(\displaystyle 1+2=3\)-at kapott és \(\displaystyle 15\)-öt adott, így neki \(\displaystyle 42\) volt, Bori \(\displaystyle 1\)-et kapott és \(\displaystyle 12\)-t adott, így Borinak \(\displaystyle 41\) volt, és András pedig \(\displaystyle 7\)-et adott, így neki \(\displaystyle 37\) volt.
(Ellenőrzés: 37, 41, 42, 40, 35, 27, 16, 2 – 30, 42, 43, 41, 36, 28, 17, 3 – 30, 30, 45, 43, 38, 30, 19, 5 – 30, 30, 30, 46, 41, 33, 22, 8 – 30, 30, 30, 30, 45, 37, 26, 12 – 30, 30, 30, 30, 30, 42, 31, 17 – 30, 30, 30, 30, 30, 30, 37, 23 – 30, 30, 30, 30, 30, 30, 30, 30.)
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173 students sent a solution. 5 points: 117 students. 4 points: 32 students. 3 points: 10 students. 2 points: 4 students. 1 point: 3 students. 0 point: 7 students.
Problems in Mathematics of KöMaL, November 2025