Another thing on my To Do list: come up with more Problem of the Week examples. (I stopped last year when I didn't get a homeroom.) I post these on my bulletin board for anyone who is interested. I enlarge the font and post the answer behind the question. Anyone have any good ones for me? Here's what I have so far: PROBLEM OF THE WEEK Twenty four red socks and twenty four blue socks are in a drawer in a dark room. What is the minimum number of socks I must take out to guarantee a match? ANSWER: 3 Either the first 2 will match, or they’ll be different. Either way, the 3rd sock will match on of the other two. PROBLEM OF THE WEEK: In one glass, there is a quantity of liquid A. A second glass holds an equal quantity of liquid B. A spoonful of A is put into glass B and stirred. Then a spoonful is taken from glass B and put into the first glass. Is there more or less of liquid A in the second glass than liquid B in the first glass, or are they equal? ANSWER: More of A in the second glass. In the first transfer, pure A went into pure B. In the second transfer, a little of that liquid was the A that had just been moved. That transfer meant that less B was taken from the second glass. PROBLEM OF THE WEEK: Four candle stubs can be melted into one new candle. If I start off with 16 candles, what is the total number of candles I can use? ANSWER: 21 Original 16: 4 + 4 + 4 + 4 ……..16 1 +1 +1 +1……….4 1…………………1 21 PROBLEM OF THE WEEK: Find a ten digit number in which: The first digit= the number of 0’s in the number The 2nd digit= the number of 1’s in the number The 3rd digit= the number of 2’s in the number And so on. ANSWER: 6 2 1 0 0 0 1 0 0 0 Logically, there HAVE to be a lot of zeros, or this will be a mess! So start with a high 1st digit, and to trial and error until you get one that works. PROBLEM OF THE WEEK: A brick weighs “6 pounds and half a brick.” How much does a brick weigh? ANSWER: 12 pounds. The other “half a brick” should weigh as much as the first half: 6 pounds! PROBLEM OF THE WEEK: Two children were playing on the toolshed roof. Something gave way, and they were dropped through the roof to the floor below. Luckily, neither was hurt. When they picked themselves up, the face of one boy was covered with grime. The other boy’s face was quite clean. Yet it was the boy with the clean face who at once went off and washed. Why? ANSWER: Each boy saw the other’s face. The boy with the clean face assumed that his face looked as dirty as that of the other boy. PROBLEM OF THE WEEK: Mr. Smith, a London businessman, went to Paris for a month’s vacation. He gave Miss Jones, his secretary, the key to his office, asking her to carry on while he was away. He also asked her to forward all letters. However, he forgot to give her the key to his mailbox. At the end of a week, he called Miss Jones and asked why he hadn’t received any of his mail. She explained that he had not left the key. He promised to forward it at once. The key was mailed, and still no mail came. When he returned home, Mr. Smith fired Miss Jones. Was he justified in doing so? ANSWER: No. He mailed the key. It ended up, with the rest of his mail, locked in the mailbox. PROBLEM OF THE WEEK: Kerry has money in her bank. She can’t make change for $1. She can’t make change for a quarter, a dime, or a nickel either. The total of her coins is $1.15. Exactly what coins are in her bank? Answer: 1 Half dollar………………………… $0.50 1 Quarter……………………………. $0.25 4 dimes…………………………….... $0.40 1 nickel……………………………… $0.05 4 pennies…………………………… $0.04 TOTAL………………………………$1.15 PROBLEM OF THE WEEK: What is the largest three-digit prime number, each of whose digits is a prime number? Answer: 753 The single digit prime numbers are 2, 3, 5, and 7. To make the largest possible prime, put the largest digits in the largest place value digits. PROBLEM OF THE WEEK. Today is Monday. What day of the week will it be in 4,902 days? ANSWER: Wednesday. Obviously, you could try to count, but that’s probably going to take some time. Since each week contains 7 days, in 7 days it will be Monday again. And it will be Monday every 7 days thereafter. Divide 4,902 by 7. It goes in 700 times (that’s 700 full weeks) with a remainder of 2. So our 4,902 days are 700 full weeks, with 2 extra days. The 2 extra days make it a Wednesday. PROBLEM OF THE WEEK: What goes up but doesn’t come down? ANSWER: Your age! PROBLEM OF THE WEEK: A soccer team just became first in the national league. The players which were on the field just after the referee blew the final signal wanted to congratulate each other by shaking hands. Assuming that each of the 11 team members shook hands with each teammate only once, How many times were hands shaken in total? ANSWER: 55. The first player shook hands with his 10 team members. The second had already done one handshake, so 9 remained. The next player had 8 remaining… 10+9+8+…1=55 PROBLEM OF THE WEEK: Correct the following problem by adding one straight line: (And, no, you can’t change the equal sign to an inequality!) 5 + 5 + 5 =550 ANSWER: 5 + 5 4 5=550 PROBLEM OF THE WEEK: Al visits his old friend Joe. Al learns that Joe has 3 children, and wishes to learn their ages. They have the following conversation: Joe: The product of their ages is 36. Al: That’s nice. But I still don’t know their ages. Joe: The sum of their ages is the same as your house number. Al: That’s nice. But I still don’t know their ages. Joe: The oldest has red hair. Al: Thanks, NOW I know their ages!! How old are the 3 kids? ANSWER:: 2, 2, and 9. Clue #1: Product is 36. Possible choices: 1, 1, 36 1, 2, 18 1, 3, 12 1, 4, 9 1, 6, 6 2, 2, 9 2, 3, 6 3, 3, 4 Clue #2: sums: 1, 1, 36:38 1, 2, 18 : 21 1, 3, 12:16 1, 4, 9 :14 1, 6, 6 :13 2, 2, 9 :13 2, 3, 6 :11 3, 3, 4 : 10 BUT he still needed more info. So the sum must be 13 (the only sum used twice.) Clue #3: There is an OLDEST child. Of the two choices (1,6,6 and 2,2,9) only the second set has an “oldest.”

PROBLEM OF THE WEEK: Kerry has money in her bank. She can’t make change for $1. She can’t make change for a quarter, a dime, or a nickel either. The total of her coins is $1.15. Exactly what coins are in her bank? Answer: 1 Half dollar………………………… $0.50 1 Quarter……………………………. $0.25 4 dimes…………………………….... $0.40 1 nickel……………………………… $0.05 4 pennies…………………………… $0.04 TOTAL………………………………$1.15 **If she has four dimes and one nickel, then she CAN make change for a quarter. These are definitely some good, challenging questions!

I have a book full of tough ones that I give as extra credit. They are worth 5 bonus points on that weeks quiz if they get them correct with the correct work shown.

Wow! I too am going to start doing a puzzle of the week. I found a book that has several good problems called The Daily Spark. They have differnt kinds (I picked up the Critical Thinking one). I like that it adds logic to the mix. For example, the first questions asks what is wrong with this deduction "Bread crumbs are better than nothing. Nothing is better than cheesecake. Therefore, bread crumbs are better than cheesecake." Some are easy, others are harder.

Those are great, Alice. Two years ago I did a problem of the week for grades K through 8 at my school. That was a lot of problems to come up with, so I backed off last year.

This is a link to the website at my university where there are lots of really cool problems. http://www.colstate.edu/mathcontest/index.php