# Monthly Archives: December 2014

## 2014 in review

The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog. Here’s an excerpt: The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 9,000 times in 2014. If it were a … Continue reading

## Nine Dates

Choose any square of nine dates from a month in a calendar. What is the absolute value of the difference of the products of the dates in the opposite corners? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Let represent the … Continue reading

## Number of Subsets

Set has a number of elements strictly between the number of elements in set and twice the number of elements in set . Set has more subsets than set (recall that the empty set is a subset of every set). … Continue reading

## Pairs of Digits

How many pairs of decimal digits exist with the property that if is an integer ending in those two digits, then ends in the same two digits? Repetition of the digits in a pair is allowed. Source: NCTM Mathematics Teacher, … Continue reading

## Sum of 1/i

Find the sum of where . Source: NCTM Mathematics Teacher, February 2006 SOLUTION Multiply both sides by The above expression hasĀ terms with the middle term equal We combine the first term to the last term, the second to the … Continue reading

## Vigornii Alphabet

In the Vigornii alphabet there are consonants and vowels. How many different arrangements of letters can be made if exactly vowels must be used and no repetition of letters is allowed? Source: NCTM Mathematics Teacher, February 2006 SOLUTION 1. Choose … Continue reading

## Octahedron

Consider a cube of side . The centers of each pair of faces of the cube sharing a common edge are connected to form a regular octahedron (a regular polyhedron with equilateral triangular faces). What is the volume of this … Continue reading

## Arithmetic sequence

The terms form an arithmetic sequence whose sum is . The terms in that order, form a geometric sequence. Find the sum of all possible values for . Source: NCTM Mathematics Teacher, February 2006 SOLUTION Let represent the common difference … Continue reading

## Loaded Dice

Two “loaded” dice each have the property that a or a is three times as likely to appear as a , or on each roll. What is the probability that a will be the sum when the two dice are … Continue reading