# Tag Archives: pattern

## Triangular Array of Numbers

If you continue the triangular array of numbers shown in the figure, what number would be directly below ? Source: NCTM Mathematics Teacher, February 2008 Solution Note that the leading numbers increase by , etc. If we follow this pattern, … Continue reading

## Square of 111,111,111

Find the exact value of . Source: NCTM Mathematics Teacher, February 2008 Solution Answer: Alternative solution Multiply the numbers manually using the old-fashioned multiplication algorithm. It should be straightforward because there is no “carry”.

## Divided by 5

Find the reminder when is divided by ? Source: NCTM Mathematics Teacher, October 2006 Solution is such a large number that it is impractical to use modulo arithmetic to find the remainder. So we are going to find the remainders … Continue reading

## Sum of Digits

Find the sum of the digits in the expression . Source: NCTM Mathematics Teacher, December 2005 SOLUTION If we multiply the numbers by hand, we have the following addition ———————————- The sum of the digits equals . Answer: Alternative solution … Continue reading

## Different Paths

We must travel from to along the lines shown. If we only allow movement upward or to the right, how many different paths are there from to ? Source: NCTM Mathematics Teacher, December 2005 SOLUTION If we fill in the … Continue reading

## House of Cards

A 4-story house of cards requires cards (as shown). How many cards are required to build a 98-story house of cards? Source: NCTM Mathematics Teacher, December 2005 SOLUTION If we number the rows from the top down as rows , … Continue reading

## Binary Pascal Triangle

Each row in a binary Pascal triangle has a on each end. Each interior value is found by taking the absolute value of the difference of the two numbers immediately above it. If the number of s and s in … Continue reading

## Up or Right

Starting at the point on the coordinate plane, a pin can be moved either to point or to point . If the pin starts at and is moved to , what is the probability that it passed through ? Source: … 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