Problem 3: A family of 25 cattle rustling brothers meets once a year to divide up their ill-gotten gains. Each brother brings in all the cattle he has stolen that year and the brothers then evenly divide up the total herd between themselves giving any remaining cattle to the cook at the end of the round-up. On the day they arrive, the cattle are divvied up and there are three cows left over. That night an argument between the brothers turns nasty and seven of them are killed. The following morning they redistribute the cattle, this time having seven cows left to give to the cook at the end of the round-up. That night the roof of the bunkhouse collapses killing another seven brothers. The following morning they re-divvy up the cattle between themselves, this time leaving ten cows left over for the cook at the end of the round-up. On the third night the cook poisons the remaining brothers taking all the cattle for herself.

How many head of cattle did the cook get?

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