Real World Problems
E-mail Magic
I received an e-mail yesterday promising to tell me my birthday if I followed the instructions. It went something like this:
Take your birth month and multiply it by 5. Then add 6. Then multiply the total by 4. Subtract 9 and multiply the result by 5. Now add the day you were born to the result. Finally subtract 75.
I followed the instructions and sure enough the answer was my birth date – totally freaky!
How did it happen? Will it always work or was this just a fluke? Explain.
Now write your own magic e-mail.
Real World Problems
Map of Counties
Consider the map of Arizona’s counties. If counties which share a common border cannot be the same color, what is the fewest number of colors needed to color the map?
How do you know?
Will this answer be the same for all maps? Explain.
Real World Problems
Gym Lockers A
The school lockers are numbered from 1-100. The janitor is cleaning them out and starts with all of the lockers open. To amuse himself, he begins and locker number two and closes every other locker, then starts at locker number 3 and opens or closes every third. This continues until he gets to the 100th locker. Are there any lockers left open? If so which ones? Explain.
Real World Problems
Gym Lockers B
In the same Gym (lockers numbered 1-100), they have decided to repair the number tags with new metal tags. How many tags with the number 5 will they need for the lockers?
Real World Problems
Pin Numbers
The Bank asks you to create a 6-digit pin #. The first entry must be a non-zero number, all other entries can be a number or letter. How many different pin numbers can you choose from?
If the bank would like to make their system more secure, without having to change very much, what options might you suggest to them? Explain.
Real World Problems
Map of States
The Governors in the Western States want to build a highway which connects all of their states (Washington, Oregon, Idaho, Montana, Utah, Nevada, Arizona, Wyoming, Colorado and New Mexico), but only crosses each shared border once, can you construct such a highway? What if California wants to join them? Can Texas or Oklahoma join too? Explain.