Monthly Archives: September 2014

Exponential Power

Which is the largest: , or ? Source: NCTM Mathematics Teacher 2006 SOLUTION One way to compare powers of different bases is to convert them to the same base by using the logarithm function. Using this procedure we obtain the following … Continue reading

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Chicken Nuggets

Chicken nuggets come in packets of , or . What is the largest number of nuggets that you cannot buy when combining various packets? Source: NCTM Mathematics Teacher 2006 SOLUTION Consider the numbers , and All even numbers greater than … Continue reading

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Shuffled Cards

Two matching decks have cards each. One deck is shuffled and put on top of the second deck. For each card of the top deck, we count the number of cards between it and the corresponding card of the bottom … Continue reading

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Do You Like Mathematics

An equal number of juniors and seniors responded to the question “Do you like math?” Each respondent said yes or no. If percent of those who said yes were seniors and percent of those who said no were juniors, what … Continue reading

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Funny Face

The radius of each small circle is of the radius of the large surrounding circle. The radius of the middle-sized circle is twice that of either small circle. What fraction of the area of the large circle is not shaded? … Continue reading

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Gas Mileage

George’s car gets more miles per gallon during highway driving than it does during city driving. Recently he drove miles on a highway and in the city and used exactly gallons of gasoline. How many miles per gallon does his … Continue reading

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Double Head

Two fair coins are flipped simultaneously. This is done repeatedly until at least one of the coins comes up heads, at which point the process stops. What is the probability that both coins came up heads on the last flip? … Continue reading

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Partition Into Triangles

A square is partitioned into non-overlapping triangles so that each of the four sides of the square is also a side of one of the triangles. The intersection of any two triangles is empty, a common vertex, or a common … Continue reading

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Divide in Half

Divide in Half How many ordered pairs of integers satisfy ? Source: NCTM Mathematics Teacher 2006 SOLUTION For to be an integer must divide evenly. ordered pairs satisfy the requirement: , and . But, I don’t know how to prove … Continue reading

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