MathDB

10

Part of 2015 Latvia Baltic Way TST

Problems(1)

hat in 1 of 100 colors, 1 girl is known to 2015 boys, 1 boy knows 2015 girls

Source: 2015 Latvia BW TST P10

12/17/2022
Is it true that for all natural nn, it is always possible to give each of the nn children a hat painted in one of 100100 colors so that if a girl is known to more than 20152015 boys, then not all of these boys have hats of the same color, and, if a boy is acquainted with more than 20152015 girls, don't all these girls have hats of the same color?
[hide=original wording]Vai tiesa, ka visiem naturāliem n vienmēr iespējams katram no n bērniem iedot pa cepurei, kas nokrāsota vienā no 100 krāsām tā, ka, ja kāda meitene ir pazīstama ar vairāk nekā 2015 zēniem, tad ne visiem šiem zēniem cepures ir vienā krāsā, un, ja kāds zēns ir pazīštams ar vairāk nekā 2015 meitenēm, tad ne visām šīm meitenēm cepures ir vienā krāsā?
combinatorics