Tag Archives: pattern

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

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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

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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

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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

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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

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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

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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

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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

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Sum of 1/i

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

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Sum of Odd Numbers

Suppose the odd numbers are grouped in the following way: What is the sum of the numbers in the tenth grouping? Source: NCTM Mathematics Teacher 2006 SOLUTION Brute force method It doesn’t take long to write out the consecutive odd numbers … Continue reading

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