## Ultramagic square

Posted on: February 11th, 2014 by
2

A 9x9 grid is filled with numbers from 1 to 81, each number occurring exactly once. The grid is said to be ultramagic if the product of numbers in row k is equal to the product of numbers in column k for each k. Can you construct an ultramagic grid? - via AMS puzzle corner

## Talmud problem

Posted on: February 10th, 2014 by
3

## Number placement

Posted on: February 4th, 2014 by
You are given a string of the form "?<?>?>?<...<?", containing n '?' symbols. Give an algorithm to replace each '?' by a unique integer from 1 to n such that all the inequalities in the string are satisfied. For example, if the given string is "?<?>?>?", your algorithm may return "2<4>3>1", but may not return "4<3>2>1". - via Algorithmic puzzles

## What is the n-th number?

Posted on: February 3rd, 2014 by
Suppose a sequence of natural numbers $a_1, a_2, a_3, \dots$ satisfies the following: 1. The sequence is strictly increasing. 2. $a_2=2$ 3. If m,n are relatively prime, $a_{mn}=a_ma_n$. Show that the only such sequence is $a_n=n$. - via Mind your decisions