Mathematical and Physical Journal
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# Problem K. 110. (January 2007)

K. 110. In Dragon Castle, 14-headed baby dragon is sleeping while mummy dragon is making pancakes. She lays them on a plate and leaves home. One head wakes up, eats 1/11 of the pancakes and falls asleep again. Then another head wakes up, eats 1/13 of the remaining pancakes and falls asleep again. Next, three heads wake up at the same time, eat 1/14 of the pancakes each, and finally they wake up the rest of the heads, too. Those who have eaten, do not get any more pancakes, the remaining 9 heads eat them all. (They do not necessarily eat the same number.) How many pancakes may have been on the plate, given that every head ate a whole number of pancakes, and if they had shared them equally, no one would have got more than 143?

(6 pont)

Deadline expired on February 15, 2007.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás: A palacsinták száma nem több, mint 14.143=2002. A palacsinták száma osztható 11-gyel, a 10/11 része osztható 13-mal. Az első két fej a palacsinták 120/143 részét hagyta meg, ami osztható volt 14-gyel, tehát az eredeti mennyiség osztható 11-gyel, 13-mal és 7-tel, tehát 7.143=1001-gyel is. Mivel a palacsinták száma legfeljebb 2002, így a tálon eredetileg 1001 vagy 2002 palacsinta volt.

### Statistics:

 120 students sent a solution. 6 points: Árva Gergő, Bellovicz Lilla, Bódis Attila, Bognár Barna, Borbíró 37 Zoltán András, Boros 001 Ágnes, Csábi Barnabás, Dávid János, Fekete Dániel, Fialowski Melinda, Ficzere Zsófia, Galambos 124 Mónika, Gerlei Klára Zsófia, Harangozó Klára, Herczeg Mónika, Kovács Anita, Kőnig Erika, Lajtai Krisztina, Lénárt Tamás, Major Bálint István, Mihálka Éva Zsuzsanna, Minya Fanni, Molontay Roland, Monostori Márton Áron, Nagy Róbert, Pasztuhov Anna, Szepes Tamás, Túri Attila. 5 points: Bakos Ádám, Dóra András, Dömötör Krisztián, Kircsi Lajos, Kiss Dávid, Kitzinger Andor, Kovács 472 Nóra Beáta, Kovács 729 Gergely, Major Péter, Szeifert Bea, Szepesvári Réka, Telekes Márton, Tímár Hajnalka, Veszelka Zoltán. 4 points: 17 students. 3 points: 19 students. 2 points: 19 students. 1 point: 19 students. 0 point: 3 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, January 2007