POW#25, due Monday 5/11
Look at a calendar for September 2004. Without telling you which dates, have your friend choose four dates that form a square as in the example shown above. If your friend tells you only the sum of the four dates, you can tell her what four dates she chose.
- Use a variable, such as d, to represent one of the dates in the square. Write expressions for the other three dates in terms of that variable.
- Find an expression for the sum of the four dates in terms of your variable. Simplify that expression.
- Starting with your sum expression, explain the steps you would take to determine the four dates. Show clearly why those steps would work.
- Choose a square of dates, calculate their sum, and use your steps from question 3 to confirm that your method leads from the sum back to the four dates you chose.
XC: Will this method work for every month of the year? Why or why not?
Hint #1: assign a variable to one of the dates, and express the other dates in terms of that variable.
I would suggest calling the smallest date d, the one in the upper left corner of the square. That way, each term in your expression will have a positive constant.
Hint #2: after you have your expression, combine like terms and see if you can do any factoring.