Monthly Archives: October 2010

9876 Power

What would be the units (ones) digit for raised to the power or ? Source: http://www.olemiss.edu 9/20/2010 Solution 30=1 34=81 38=6561 312=531441 316=43046721 31=3 35=243 39=19683 312=1594323 317=129140163 32=9 36=729 310=59049 314=4782969 318=387420489 33=27 37=2187 311=177147 315=14348907 319=1162261467 Notice that … Continue reading

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First Term

In an arithmetic sequence of positive whole numbers, the common difference is twice the first term of the sequence.  If the sum of the first six terms is equal to the square of the first term of the sequence, what … Continue reading

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823

Let  and represent different positive integers.  Find the value of and if ? Source: mathcontest.olemiss.edu 10/25/2010 Solution  is a prime number, that is . We can write Therefore, and .

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100737

P and Q represent different positive integers.  Find all values of both P and Q such that the product of the product of P and Q and the difference of P less Q is equal to 100737.  In other words, … Continue reading

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Three Not Two

Find the sum of all positive integers less than 10,000 that are divisible by three but not divisible by two. Source: mathcontest.olemiss.edu 10/4/2010 Solution STEP 1 Understand the problem 3 is divisible by 3 but not by 2, so 3 … Continue reading

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Roll That Die

Roll That Die A fair six-sided die is rolled 6 times.  What is the probability of rolling a number greater than four at least five times? Source: mathcontest.olemiss.edu 9/27/2010 Solution Let’s start by working on a simpler problem. Let’s roll … Continue reading

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