MathDB

1

Part of 1976 Putnam

Problems(2)

Putnam 1976 A1

Source:

4/18/2022
PP is an interior point of the angle whose sides are the rays OAOA and OB.OB. Locate XX on OAOA and YY on OBOB so that the line segment XY‾\overline{XY} contains PP and so that the product (PX)(PY)(PX)(PY) is a minimum.
college contests
Putnam 1976 B1

Source:

4/18/2022
Evaluate limn→∞1n∑k=1n([2nk]−2[nk])lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^{n} ([\frac{2n}{k}] -2[\frac{n}{k}]) and express your answer in the form log⁡a−b,\log a-b, with aa and bb positive integers. Here [x][x] is defined to be the integer such that [x]≤x<[x]+1[x] \leq x <[x]+1 and log⁡x\log x is the logarithm of xx to base e.e.
college contests