Volume 56
, Issue 3

2020

Dear Reader, welcome to this issue of Parabola!
It is my pleasure to dedicate this issue to Bruce Henry, to whom I - and Parabola - owe much. It also my pleasure to welcome Parabola's newest Problem Editor, Sin Keong, a life-long expert in Parabola problems.

The number $1 + \sqrt{2}$ has an interesting property. When we calculate the numbers

$1 + \sqrt{2}$, $(1 + \sqrt{2})^2$, $(1 + \sqrt{2})^3$, $\ldots$,

they seem to get closer and closer to integers.

In this paper, I will share how to use and optimize Monte Carlo Integration to solve a real-world problem.

This paper analyzes game in which the player knows possible payoffs and their possible moves but does not know the game mechanisms. We analyze how learning is acheived, not by learning game mechanisms, but by players geting better at guessing their way through repetitions, based on their prior results.

Consider the algorithm CARA: take a number, count the number of letters in its spelling to get a new number, and repeat. For example,

15 (fifteen) → 7 (seven) → 5 (five) → 4 (four) → 4 (four) → ···

We show that all such sequences end in the number 4.

In this article we present brief summaries of some mathematical articles which readers may be interested in. If this list of readings proves popular, it may become a regular feature in Parabola.

An odd comic about even numbers.

Q1639 What is the largest integer that cannot be expressed as $99a+100b+101c$, where $a$, $b$, and $c$ are non–negative integers?