2013 Mathematics Game

feature photo above by Alan Klim via flickr

New Year’s Day

Now is the accepted time to make your regular annual good resolutions. Next week you can begin paving hell with them as usual.

Yesterday, everybody smoked his last cigar, took his last drink, and swore his last oath. Today, we are a pious and exemplary community. Thirty days from now, we shall have cast our reformation to the winds and gone to cutting our ancient shortcomings considerably shorter than ever. We shall also reflect pleasantly upon how we did the same old thing last year about this time.

However, go in, community. New Year’s is a harmless annual institution, of no particular use to anybody save as a scapegoat for promiscuous drunks, and friendly calls, and humbug resolutions, and we wish you to enjoy it with a looseness suited to the greatness of the occasion.

— Mark Twain
Letter to Virginia City Territorial Enterprise, Jan. 1863

For many homeschoolers, January is the time to assess our progress and make a few New Semester’s Resolutions. This year, we resolve to challenge ourselves to more math puzzles. Would you like to join us? Pump up your mental muscles with the 2013 Mathematics Game!

Continue reading 2013 Mathematics Game

2012 Mathematics Game

photo by Creativity103 via flickr

For our homeschool, January is the time to assess our progress and make a few New Semester’s Resolutions. This year, we resolve to challenge ourselves to more math puzzles. Would you like to join us? Pump up your mental muscles with the 2012 Mathematics Game!

Rules of the Game

Use the digits in the year 2012 to write mathematical expressions for the counting numbers 1 through 100.

Bonus Rules
You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.

You may use multifactorials:

  • n!! = a double factorial = the product of all integers from 1 to n that have the same parity (odd or even) as n.
  • n!!! = a triple factorial = the product of all integers from 1 to n that are equal to n mod 3

[Note to teachers: Math Forum modified their rules to allow double factorials, but as far as I know, they do not allow repeating decimals or triple factorials.]

Continue reading 2012 Mathematics Game

2011 Mathematics Game

[Photo from Wikipedia.]

Two of the most popular New Year’s Resolutions are to spend more time with family and friends, and to get more exercise. The 2011 Mathematics Game is a chance to do both at once.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

Here are the rules:

Use the digits in the year 2011 to write mathematical expressions for the counting numbers 1 through 100.

  • All four digits must be used in each expression. You may not use any other numbers except 2, 0, 1, and 1.
  • You may use the arithmetic operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial). You may also use parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .1, .02, etc.
  • Multi-digit numbers such as 20 or 102 may be used, but preference is given to solutions that avoid them.

Bonus Rules
You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.

You may use multifactorials:

  • (n!)! = a factorial of a factorial, which is not the same as a multifactorial
  • n!! = a double factorial = the product of all integers from 1 to n that have the same parity (odd or even) as n
  • n!!! = a triple factorial = the product of all integers from 1 to n that are equal to n mod 3

[Note to teachers: The bonus rules are not part of the Math Forum guidelines. They make a significant difference in the number of possible solutions, however, and they should not be too difficult for high school students or advanced middle schoolers.]

Continue reading 2011 Mathematics Game

2010 Mathematics Game Update


[Photo by pfala.]

Thanks to John Cook’s article about factorials in the recent Mathematics and Multimedia Carnival, we’re adding new rules to the 2010 Mathematics Game.

Let’s play with multifactorials!

Continue reading 2010 Mathematics Game Update

2010 Mathematics Game


[Photo by pfala.]

Did you know that playing games is one of the Top 10 Ways To Improve Your Brain Fitness? So slip into your workout clothes and pump up those mental muscles with the 2010 Mathematics Game!

Here are the rules:

Use the digits in the year 2010 to write mathematical expressions for the counting numbers 1 through 100.

  • All four digits must be used in each expression. You may not use any other numbers except 2, 0, 1, and 0.
  • You may use the arithmetic operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial). You may also use parentheses, brackets, or other grouping symbols.
  • You may use a decimal point to create numbers such as .1, .02, etc.
  • Multi-digit numbers such as 20 or 102 may be used, but preference is given to solutions that avoid them.

Bonus Rule
You may use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal.

[Note to teachers: This rule is not part of the Math Forum guidelines. It makes a significant difference in the number of possible solutions, however, and it should not be too difficult for high school students or advanced middle schoolers.]

Continue reading 2010 Mathematics Game

2009 Mathematics Game

new-year
[Photo by Amanda M Hatfield.]

Have you made a resolution to exercise your mental muscles this year? Then please join us for the 2009 Mathematics Game. Here are the rules:

Use the digits in the year 2009 and the operations +, -, x, ÷, sqrt (square root), ^ (raise to a power), and ! (factorial) — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.

  • All four digits must be used in each expression.
  • Only the digits 2, 0, 0, 9 may be used.
  • The decimal point may be used, as in .9, .02, etc.
  • Multi-digit numbers such as 29 or 902 may be used, but preference is given to solutions that avoid them.

By definition: 0! = 1 .
[See Dr. Math’s Why does 0 factorial equal 1?]

For this game we will accept: {0}^{0} = 1 .
[See the Dr. Math FAQ 0 to the 0 power.]

Continue reading 2009 Mathematics Game