Math Puzzle of the Month of June 2012

May 13, 2012
Here's the solution to the puzzle of March:

 The point is that you need to arrive at a situation where "either the fake coin is lighter and is one of these coins; or the fake coin is heavier and is one of those coins".

The first weigh is: 4 vs 4

We will consider 2 cases:

A) the left side is heavier than the right side
B) the two sides are of the same weight

for A) the fake coin is on the scale, that means the remaining coins are all real, for ease of explanation we name the coins as follows:

H1, H2, H3, H4, L1, L2, L3, L4, R1, R2, R3, R4

where H1, H2, H3, H4 are the coins on the heavier side; L1, L2, L3, L4 are the coins on the lighter side; and R1, R2, R3, R4 are the remaining real coins. In this situation, we know that the fake coin is either heavier and is one of H1, H2, H3, H4; or lighter and is one of L1, L2, L3, L4.

We do the second weigh as follows:

H1,H2,L1,L2 vs H3,L3,R1,R2

we have 3 cases:

C) the left side is heavier
D) the right side is heavier
E) the two sides weighs the same

for C) the fake coin is either H1, H2 or L3 (can you figure out why?) the final weigh will be H1 vs H2 and you can get the answer

for D) the fake coin is either L1, L2 or H3, the final weigh will be L1 vs L2 and you can get the answer

for E) the fake coin is either H4 or L4, the final weigh will be H4 vs R1 and you can get the answer

Hence case A) is complete, we now deal with case B), in this case the coins on the scale are real, and one of the remaining coins is fake, we name the coins as follows:

R1, R2, R3, R4, R5, R6, R7, R8, U1, U2, U3, U4

where the R's are the real coins and the U's are the remaining coins.

We do the second weigh as follows:

R1, R2, R3 vs U1, U2, U3

we have 2 cases:

F) the left side is heavier (that the right side is heavier is similar)
G) the two sides weights the same

for F) the fake coin is lighter and is one of U1, U2, U3. We weigh U1 vs U2 and we can get the answer

for G) the fake coin is U4, but we don't know whether it it is lighter or heavier than the real ones, we can find this out by weighing this against one of the real coins.

This is the solution for a 12 coin problem, the second weigh of case A) is the tricky weigh.

In general, if you are allowed to weigh n times, then the maximum number of coins that you can play with is ((3 ^ (n - 1)) - 1) * 3 / 2


Now, the puzzle of June 2012:

You are told to find the value of x in this equation:

2x^2+5x-3=0

Good luck!

 
 

Happy Mother's Day!

May 13, 2012
Happy Mother's Day!

Hope you all are having a good time!  I'm here to tell every mom it's Mother's Day.  Go ahead, take a look:

I'm fast asleep,
It's time for school.
My mother is
My wake-up tool.
I'm getting hungry,
What do I see?
My breakfast is ready,
Mom made that for me!
The car is speeding
Across the land.
Driven by
My mother's hand.
I'm at school,
With nothing to ask.
I'm at my desk
Working on my task.
We eat inside,
Since there's a storm.
My mom hands my lunch,
Still nice and warm.
School is over.
I'm glad to come home.
It's like living
In a mini biome.
So this is the way
I would like to conclude.
My mother keeps me
In a really good mood.

HAPPY MOTHER'S DAY!

 
 

April Fools Day

March 30, 2012
April Fools Guys!

Hope you had a great March!  Now that April is swooping in, why not start off the month with some April Fools, as it always does!  Here is a poem to get us started up for the new month; April!

 April Fools
They’re made to fool me,
Not so cool
They can’t control me.
April Fools
Is in the morning,
Once again
They’re not adorning.
April Fools
In my locker,
Even when
I go play soccer.
Spiders
They’re behind your head,
Snakes
Are underneath your bed.
Pranks are played
It’s in the air
Tricks are played
They’re everywhere
April Fools
I’m coming home,
Silly string
All over my comb.
April Fools
I’m in my room,
My sister has
A snake costume.
April Fools
She jumps inside,
Towards the place
I meant to hide.
April Fools
I peek outside,
She’s pulling
All of my coverings aside.
April Fools
“I’ve lost my pride,”
“April Fools!”
My sister replied.
April Fools
They’re made to fool me,
Not so cool
They can’t control me.

Thanks for listening to my poem, guys!  It's going to be a great April this year, I can promise that!
 

Solution to Math Puzzle of the Month of January 2012 and Math Puzzle of the Month of March 2012

February 28, 2012
Hello everyone. Sorry about missing out on the "Math Puzzle of the Month of February 2012", but, anyways, this is the solution to the puzzle of January.

The last month on the calendar is July 2014.  If you look at it all of the titles are blue violet except for 28 titles.  This means all of them are of July except for 28 months.  In one year, 11 months would not be July.  How many times can 11 fit into 28?

28 / 11 = 2 R6

Okay. This means that so far, two years have passed.  The next month is January 2014.  Now we have to deal with the remainder of 6.  Well, six months other than July would go to June 2014.  But it doesn't end there.  It can also be July 2014 because there are six more months other than July.  Our two possibilities left are June 2014 and July 2014.  In order to settle it, we use the other set of information.  The other set says that all of the titles are blue except for 29 titles.  This means all of them are of August except for 29 months.  In one year, 11 months would not be August.  How many times can 11 fit into 29?

29 / 11 = 2 R7

Okay. Once again, this means so far that two years have passed.  The next month will be, as we already have discovered, January 2014.  Time for the final decision.  Is it June 2014 or July 2014?  The remainder determines it all.  There are seven months other than August, and that goes down to July 2014.

Here is the Math Puzzle of the Month of March 2012.

There are twelve tennis balls in front of you.  You are told to weigh them.  You can only use the scale three times.  You must figure out which tennis ball is the different one and if it is heavier or lighter than the others.

Overall job for you to do:  Discover how to do it.  There is a formula.

(Note:  Do not try weighing the tennis balls.  You do not know heavy each one is.  Just come up with the formula.) 

 

D.A.R.E. Poem

January 21, 2012
    D.A.R.E. is a program throughout the city of Irvine to help kids recognize that they must be drug free in order to live a better and healthier future.  At my school, you create a project in December to demonstrate a strong, clear, drug fee message.  You have three options on what to make.  They are a poster, a poem, or an essay.  I chose to make a poem for my D.A.R.E. project because I thought that I had a pretty good talent of poetry.  Here was my poem:

Drugs are where things fall apart,

Avoid them to get a big head start.

There’s a huge list of them that come your way,

All you’ve got to do is say no and turn away.

Some of them may ruin your lives,

Just know what to do when the situation arrives.

Don’t get sick nor catch any disease,

Just make good choices and it should be a breeze.

Smoking tobacco can cause tons of damage,

Just avoid it and treat it like bad ravage.

Then comes another one; it’s a marijuana cigarette,

These can especially make your body upset.

Alcohol and beer can make you turn drunk,

Just say no and describe it as junk.

Basically, just try to stay drug free,

Make reasonable choices and avoid debris.

Drugs will damage your body seriously,

Physically, socially, mentally, and emotionally.

Lastly, do not let others define your life for you,

Make your own choices and know what to do.

I submitted the poem above only hoping to become the winner.  Fortunately, I did win first place!  The poem could have been longer (since I love making my poems as long as possible), but this was the maximum length of the poem requirements.  Hope you enjoyed reading!
 

Math Poem and Trick

January 8, 2012
Hello, everybody!  As you know, I am very passionate for mathematics.  I decided to create a poem about math.  Enjoy!

Math is not just numbers and signs,
Instead it's patterns that our world defines.
Look around you; shapes and sizes,
Look at the Earth's many prizes.
Math is something that establishes connections,
Check out all of math's different sections.
Variables and coefficients in algebra,
Geometry that describes a parabola.
Add, subtract, and more in computation,
Simplifying expressions with calculation.
Math is more than solving situations,
More than calculus of variations.
Math is what builds all foundations,
It's what simplifies any operations.
Math has been working for generations and generations,
And with it you can exceed all expectations.
Think again, now, math is very useful,
I'm not kidding; I'm being truthful.
Now it's time to conclude what's here,
That's all I've got for you to hear.

That's right!  Did you know that if you ask somebody a simple question, you can tell how well they do in mathematics.  The question is, "What is math?"  It might seem impossible at first, but it actually works.

For example, most people will just say, "numbers," "a lot of rules," or "a subject."  The best possible answer would be something like, "patterns and connections and how they interact with each other."  But then again, a long answer doesn't necessarily mean it's a good answer.  So just keep in mind this one sentence: "Whatever you think math is, math shows it when you calculate for an answer."  Thanks!
 

Solution to December 2011 Puzzle and Math Puzzle of the Month of January 2012

December 31, 2011
Solution for December:

 There are 44 kids in the circle.  If you think about it, a circle with 4 children will have the 1st kid opposite the 3rd, and the 2nd kid opposite the 4th.  If I told you only that the 2nd kid is opposite of the 4th, you would solve it like this:

4 (4th child) - (opposite of) 2 (2nd child) = 2 (2 kids inside half of the circle)
2 (2 kids inside half the circle) * 2 = 4 (4 kids in the entire circle)

The same math applies for the math puzzle of the month:

29 - 7 = 22
22 * 2 = 44

Congratulations to all who solved the math puzzle correctly!  Now for the math puzzle of the New Year!

Math Puzzle of the Month of January 2012


 A calender is hanging on your fridge.  Each month is on a separate page and each page's title is in a different color.   For example, January could be green.  If January 2012 is green, then January 2013 must have a green title as well.  No other month on the calendar except January can be green. The calendar starts on January 2012.  You want to know what month is the last month on your calendar.  Here is the coloring:

January = Green

February = Magenta

March = Yellow

April = Pale Tan

May = Orange

June = Fire Truck

July = Blue Violet

August = Blue

September = Light Turquoise

October = Pumpkin

November = Silver

December = White

If all of the titles are blue except for 29 titles, and all of the titles are blue violet except for 28 titles, what is the last month on your calendar?  (Note: Month and year required in answer.)

Good luck!  Happy New Year!
 

Math Puzzle of the Month of December 2011: Ring of Children

December 1, 2011
Some children were standing in a circle.  The 7th was standing opposite of the 29th kid.  How many kids are in this ring?
 

Spying on A Random Car

November 30, 2011
Wow!  This 0:27 video of me spying on a random car is completely worth a watch.  Even if you don't have sound, don't worry, there's sub quotes in the video itself.  Enjoy!  The link is http://www.youtube.com/watch?v=h5vOUh3pz6M.
 

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About Me


I'm a 11-year-old resident of Irvine, California who loves mathematics. Let me tell you, I really like math. Calculations are really easy for me, but that's not it. I also get straight A's on all the other subjects like science, which is my second favorite subject, reading, music, social studies, and more. I'm a guy who wants to handle statistics when I grow up, or I could be a chemist. I am also eager for a great future. My name is Omar Mughal, and that's about me!

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