EVENTS

 

January 5th, 2015: 15-Minute Meeting - AMC12

 

Today we met for literally 15 minutes to end off the semester. We went over the PDF file concerning the AMC12 which can be found on the "AMC 12" tab on this website. Our contest will be on February 3rd, 2015 at 4:00 PM. You can bring friends to take the contest. It is only 75 minutes of your time. Be mindful that February 3rd is a permanent date but the time that day is bound to change. As of now it is 4:00 PM. We will keep you updated if any changes are made. We also handed out the 2007 AMC 12 Contest Questions from Version A so that you guys can do some practicing. In order to save paper, we sent out the solutions by email but they can also be found here. If you want more practice, you can find it at the "Art of Problem Solving" Website! 

Some Advice:

  • You have 3 minutes per question and no penalty if you leave a question blank (you actually get 1.5 points) and no penalty if you answer incorrectly. So, if you find yourself stuck on a problem, do not give it more than its 3-minute time limit and move on to the next one. Leave it blank and you just gained yourself an extra 1.5 points!!
  • Draw pictures and try to think of the problem on many levels not just the mathematical level.
  • DO NOT over think the problems
  • Because the questions range in order of difficulty, you should probably leave the last ten or so blank.
  • If you want to make it into the AIME, you will need to score at least 100 points or be in the top 5% percent. You can easily achieve this by answering 14 questions correctly, 0 incorrectly and leave the rest (11) blank. The first 14 questions will be the easiest so answer those correctly and leave the rest blank and voila! You are in the AIME with a score of 100.5!!

 

December 28th, 2014: No Meeting - Winter Break 

 

December 22nd, 2014: Club Photo & ORIGAMI STARS

 

Today, we started off by fetching some photographers roaming around the hallways to take our club photo for the 2014-2015 Yearbook. Thanks to Alex Komanoff, Caroline Nelson and Sarah Allen for the great photo. Then, we went over some AMC 12 problems that students have been struggling with. Finally, for a change,we made ORIGAMI STARS using 3"x3" colorful papers and the following template. We started off with 6 sheets of paper and some of us even got crazy and made the stars with 10 sheets!! It was an extremely fun activity. You may be wondering: How does this relate to math?!? Well, don't worry!! Attached you will find a document about Trisecting Angles! Here is a picture of an Origami Star made by a club member using 8 sheets of paper.

 

 

December 8th, 2014 and December 15th, 2014: Mock AMC 12

 

For these two weeks, we focused on AMC 12 problems from previous years. The AMC 12 is a 25-multiple choice question, 75-minute math competition for students of 12th grade (Y2) and under. The questions are mostly algebra and geometry problems, with some probability questions thrown in the mix. To qualify for the American Invitational Mathematics Examination (AIME), you need to get a little more than half of the problems right. 

 

During club meetings, we split up into teams and went through selected problems. The team who got the question correct first received a point and the team with the most number of points in the end got a prize (of food). 

 

One of the problems we got stuck on was this: 


Three positive integers are each greater than 1, have a product of 27,000 and are pairwise relatively prime. What is the sum of these integers?
 

Hint: Relatively prime means that the GCF of two numbers is 1, but that doesn't mean the numbers themselves are prime. For example, 10 and 21 are relatively prime, but neither are prime. 

 

Can you solve the problem?

 

December 1st, 2014: Logic Puzzles and SPORCLE

 

This week, we worked on some Logic Puzzles obtained from Stella's Book, IQ Challenge. We also introduced people to a very fun and diverse website known as Sporcle. We began by solving a Sporcle Math Puzzle together and then passed out some logic puzzles and continued to do them!

 

November 24th, 2014: There Was No Meeting Today

 

November 17th, 2014: Paradoxes

 

The theme of the week was paradoxes. A paradox is something that has an answer that seems illogical, but nevertheless is correct. The first one we looked at was the Monty Hall paradox. It is based on the TV show Let's Make a Deal. In the show, you have to pick amongst three doors not knowing what is behind them and you get whatever is behind the door you pick. One of the doors has something good (ex: car) and the other two doors have something bad (ex: goat). The host opens one of the doors that you did not pick which has a goat. With your door and one other door left, the host asks do you want to stick with the door you picked or switch and pick the other door left. What should you do? It seems that it would be a 50-50 chance for either option, but actually you are more likely to get the car if you switch doors. The reasoning behind this is explained here.

 

The other paradox we looked at was the birthday paradox. The question was how many people do you need to have in a room so that there is a 50% chance that two of the people in the room share the same birthday? The answer is best explained here. 

 

November 10th, 2014 : Arithmetic Tricks

 

Our theme this week was arithmetic tricks. We all dread doing mental math, especially with large numbers, but there are some tricks that make it effortless. On the surface, they appear almost magical. Nevertheless, if you dig deeper into the algebra behind it, it all makes sense.

 

One example of this mental math trick is multiplying a 2-digit number by 11. For 45 x 11, you sum up the two digits, 4 and 5, and squeeze it between the number 45. So, 45*11 =  495.

 

Is it magic or math?

 

Turns out, it’s the latter. 45*11 is the same as (40+5)(10+1). By the FOIL method, it equals 40*10 + 5*10 + 40*1 + 5. The middle two terms, 5*10 + 40*1, can be rewritten as 10(5+4), which explains the summing of the two digits and the placing of it in the tens digit. The 40*10 and the 5 explain why the 4 in 45 moves to the hundreds place and the 5 stays in the ones place.

Additionally, we analyzed what went wrong in proofs that lead to astonishing conclusions. For one of them, 4 ended up equaling 5. In another, 1 = 2. See if you can find why math is still trustworthy after all. (Hint: Some things are seem equal but violate rules of arithmetic.)

 

 

November 3rd, 2014 : Domineering

 

This week we played a game called domineering, which is a pencil and paper game that involves two players. One player connects two adjacent dots on the grid horizontally and the other connects them vertically. Once one dot has been connected by a line, no other line can be connected to it. The players take turns until one player can not make any more movements. The person who made the last move is the WINNER!!

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October 27th, 2014 : Einstein Puzzles

 

As we celebrated our amazing club leader’s birthday (Reham), we solved Einstein puzzles. Supposedly these puzzles were created by Einstein himself and that 98% of the population cannot figure them out. I don’t know whether these claims are factual, but that doesn’t affect our enjoyment of them. In short, Einstein puzzles use logical deductions to figure out certain qualities about someone. There are clues about the given individuals’ favorite items or likes, as well as something about who they are.

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October 20th, 2014 (First Meeting!) : Triangular Peg Solitaire

 

This was our first meeting of the year. We decided to just speak about what we do as the school's math club, welcome returning and new members, then went on to have a little fun playing Triangular Peg Solitaire. This game was proposed to us by co-leader Stella who said that she encountered and later became obsessed with this game in the Southern-country-themed restaurant Cracker Barrel. This is a one-player game in which a valid move is to jump a peg orthogonally over an adjacent peg into a hole two positions away and then to remove the jumped peg. The goal is to end up with only 1 Peg on the board. We drew 15 circles arranged in a larger triangular form and used that as a template for the game while chocolate Hershey Kisses were used for the pegs. After playing countless rounds, we rewarded ourselves with the 14 chocolate kisses that we used as pegs and believe us... the kisses tasted GREAT!

 

 

 

 

 

 

 

All Rights for the images reserved to Petras Gagilas photostream from flickr, if you keep them,please keep the credit.

bardmaticians@gmail.com  | 525 East Houston Street, Room 410, New York, NY, 10002 |

 

 

 

 

 

Bardmaticians 

Mondays in Room 410 

3:30 PM to 4:30 PM

 

 

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