MathDB

2

Part of 1997 Putnam

Problems(2)

Putnam 1997 B2

Source:

5/30/2014
ff be a twice differentiable real valued function satisfying f(x)+f′′(x)=−xg(x)f′(x) f(x)+f^{\prime\prime}(x)=-xg(x)f^{\prime}(x) where g(x)≥0g(x)\ge 0 for all real xx. Show that ∣f(x)∣|f(x)| is bounded.
Putnamfunctioncollege contests
Putnam 1997 A2

Source:

5/30/2014
Players 1,2,…n1,2,\ldots n are seated around a table, and each has a single penny. Player 11 passes a penny to Player 22, who then passes two pennies to Player 33, who then passes one penny to player 44, who then passes two pennies to Player 55 and so on, players alternately pass one or two pennies to the next player who still has some pennies. The player who runs out of pennies drops out of the game and leaves the table. Find an infinite set of numbers nn for which some player ends up with all the nn pennies.
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