Digital Commons Network^™

Math Puzzler, Paul J. Tobias

Humanistic Mathematics Network Journal

No abstract provided.

The Study Of Mathematics And Growth In The Spirit, Rosemary Schmalz

Humanistic Mathematics Network Journal

No abstract provided.

Analysis Of A Recurrence Arising From A Construction For Nonblocking Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

Define f on the integers n > 1 by the recurrence f(n) = min( n, min_m|n( 2f(m) + 3f(n/m) ). The function f has f(n) = n as its upper envelope, attained for all prime n.

The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form f(n) ~ C(log n)^{1 + 1/γ} for certain constants γ and C, in the sense that for any ε > 0, the inequality f(n) ≤ (C + ε)(log n)^{1 + 1/γ} holds for infinitely many n, while f(n) ≤ (C + ε)(log …

Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93

All HMC Faculty Publications and Research

The game Klappenspiel ("flipping game") is a traditional German game of flipping tiles according to dice rolls. In this paper, we derive the optimal strategy for this game by using dynamic programming. We show that the probability of winning using the optimal strategy is 0.30%.

Analysis Of A Recurrence Arising From A Construction For Non-Blocking Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

Define f on the integers $n > 1$ by the recurrence $f( n ) = \min \{ n,\min _{m|n} 2f( m ) + 3f( n/m ) \}$. The function f has $f( n ) = n$ as its upper envelope, attained for all prime n. The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form $f( n ) \sim C( \log n )^{1 + 1/\gamma } $ for certain constants $\gamma $ and C, in the sense that for any $\varepsilon > 0$, the inequality $f( n ) \leq ( …