Idaho
Society of Professional Engineers
PO Box 170239, Boise, ID 83717-0239 208-426-0636 Fax: 208-426-0639 E-Mail: ispe@idahospe.org
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PO Box 170239, Boise, ID 83717-0239 208-426-0636 Fax: 208-426-0639 E-Mail: ispe@idahospe.org |
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Idaho Society of Professional Engineers
• April 23 & 24, 2007 –
2007 Western and Pacific
Regional Conference – Las Vegas, Nevada • May 11, 2007 – National MATHCOUNTS Competition – Convention Center, Fort Worth, Texas
• May 11, 2007 – ISPE Southwest Chapter Spring Fundraiser Golf Tournament - 4-Person Scramble - 1:00 PM - Purple Sage Golf Course
Prime Time
What is the greatest positive difference between two prime numbers whose sum is 18? -------------------------------------------------------------------------------- Which two-digit even whole number can be expressed as the sum of two prime numbers whose positive difference is the greatest? -------------------------------------------------------------------------------- Another conjecture called the “Weak conjecture” stated by Goldbach says that any odd integer greater than 5 can be expressed as the sum of 3 prime numbers? In how many ways can 21 be expressed as the sum of 3 prime numbers? -------------------------------------------------------------------------------- In the 18th century Leonhard Euler stated a formula to generate prime numbers. The formula is : P(x) = x2 + x + 17, where x is a whole number. What is the least whole number n such that P(n) is not prime?
Answer to last week’s MATHCOUNTS problem: The area code is of the form NXX where N is a digit from 2 through 9 and X is a digit from 0 through 9. There are 8 possibilities for N and 10 possibilities for X. 8 × 10 × 10 = 800. There are 800 possible three-digit area codes and there are 800 possible three-digit prefixes. There are 10 × 10 × 10 × 10 = 10000 possible four-digit line numbers. There are 800 × 800 × 10000 = 6,400,000,000 = 6.4 ×109 possible ten-digit phone numbers. -------------------------------------------------------------------------------- There are 283 area codes. For each area code there are 8 × 10 × 10 = 800 three-digit prefixes and there are 10 × 10 × 10 × 10 = 10000 possible four-digit line numbers. There are 283 × 800 × 10000 = 226,400,000,000 possible phone numbers. There are enough phone numbers available so that every US citizen can have their own phone number. --------------------------------------------------------------------------------
The state with the greatest population in people to the number of area codes is California. Note that four of the states (Florida, Ohio, Pennsylvania, and Texas) have population, in people, to the number of area codes rates that are about 1,000,000 people to 1 area code. California and New York have population, in people, to the number of area codes rates that are greater than 1,000,000 people to 1 area code and are the rates that need to be checked to answer the question.
If you want to see last week's problem again, click http://www.mathcounts.org/webarticles/anmviewer.asp?a=996&z=110
Idaho Society of Professional Engineers
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National Engineers Week - Future City Competition
Board of Professional Engineers and Professional Land Surveyors
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