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Classic Math Problems Here is a collection of math problems that I think every student in the United States should experience at some time (or several times) in their educational journey. Grades K-4 Add all the integers from 1 to 100 - Find the sum of all the integers (no decimals or fractions) from 1 to 100. Double your money - A daughter and her father agreed that she should get some allowance for doing dishes. The daughter had two proposals for how she would get paid. Proposal #1 -
$100 every day for a month (31 days) Which method would you take? Grades 5-8 The rabbit problem - Laura was training her pet white rabbit, Sugar, to climb a set of 10 steps. Sugar can jump one or two steps at a time, but never goes back down. How many different ways can Sugar get to the top of the stairs? Add all the integers from 1 to 1,000 - Find the sum of all the integers (no decimals or fractions) from 1 to 1,000. Tower of Hanoi - There are three poles. On the middle pole, there are thirty disks, with each one being a little smaller than the one below it. Your job is to move the entire stack of disks to another pole, but you must follow the rules. You can only move one disk at a time. You can never put a larger disk on top of a smaller disk. The disks must be moved from pole to pole. How many moves are necessary to accomplish this feat? Pascal's Triangle - Figure out the pattern. Find 10 different patterns and explain each pattern.
1 ? ? ? ? ? ? Grades 9-12 The rope around the earth problem - A rope is snugly tied around the equator. The rope is cut and then one meter is added to its length. The rope is then redistributed evenly all along the equator. Question: How far off the ground will the new rope be? The handshake problem - There are 200 people in a room. Everyone introduces themselves to every other person in the room. How many handshakes will there be all together? The pizza problem - A large pizza is going to be cut into pieces. What is the maximum number of pieces it can be cut into using straight cuts? The board problem - It takes 12 minutes to cut a board into 4 pieces. Assuming it's the same kind of board and saw, how long would it take to cut a board into 10 pieces? The missing speed - A car was going to travel a distance of 2 miles. For the first half of the trip, the car was going 40 miles per hour. The driver wanted to average 50 miles per hour for the entire trip. What speed is necessary to make that average for the entire trip? The water and the wine - A glass of water and a glass of wine are on a table. A tablespoon of water is taken from the glass of wine and transferred to the glass of water. The water is then stirred up before a tablespoon of water is transferred back to the glass of wine. Question: Is there now more water in the wine glass, or wine in the water glass? (Forget for a moment that wine is mostly water). Proof that 2 = 1. Can you figure out what's wrong? Follow this link to 2 = 1. The Locker Problem - There are 1,000 lockers at your school. One day, the principal had a creative thought about testing these lockers. The first student would open every locker door. The second student would close every other door. The third student would either open or shut every third locker door. The fourth student changes every fourth, etc. Which doors would remain open after 1,000 students changed the doors in this manner? (updated 6-3-99) |