The Missing Peso

This paradox probably has thousands of variants already. Since the concept is no longer original, I will reinvent the presentation by introducing one of my favorite comfort foods: yogurt!

~o~o~

After watching a rather depressing film, three friends decided to share a yogurt which costs PhP 145. Each one of them gave the cashier a 50-bill. In return, the cashier hands them five 1-peso coins as change. Each of them takes one of the coins and deposits the remaining two coins in the tip box. When seated, one of the girls did a simple math. Each girl's share is PhP 49, giving a total of PhP 147 for the three of them. Add the PhP 2 tip to this gives only a total of PhP 149. Where is the other 1-peso? Explain this paradox.

~o~o~

The problem was presented in a way the readers would think that there is a missing peso, when in fact what is really missing is logic. In truth, the transaction is balanced; think of inflow-outflow, or cash flow analysis. The yoghurt costs PhP 145; 1 peso was returned to each of them for a total of 3 pesos; they dropped 2 pesos on the tip box. The sum of these amounts is PhP 150. Equivalently, each of them contributed only PhP 49 giving a total of PhP 147 and the yoghurt plus the tip equals PhP 147. Thus, every peso has been attributed for.

By the way, the yogurt is worth fighting the missing peso for! Visit Red Mango for proof.

[Photo from Red Mango Philippines Facebook]

Funny Maths

After a day of chanting formulas in my head, solving exam problems and finishing up a proposal due today, I sensed a migraine coming. Fortunately, these jokes saved me from chugging down a painkiller or two and restored my sanity. Laughter is no doubt the best medicine! Photos taken from http://www.tanyakhovanova.com/Jokes/pictures.html.

A-Kira-and-Kevin Problem

This is one of those Kira and Kevin problems found in the Exam MLC Actuarial Models. This particular question really pissed me off the first time I tried it because it took me a looong time to solve. This is easy though, if you are familiar with the concept of a joint-life status.

Kevin and Kira excel at the newest video game at the local arcade, "Reversion". The arcade has only one station for it. Kevin is playing. Kira is next in line. You are given:

1. Kevin will play until his parents call him to come home.
2. Kira will leave when her parents call her. She will start playing as soon as Kevin leaves if he is called first.
3. Each child is subject to a constant force of being called: 0.7 per hour for Kevin; 0.6 per hour for Kira.
4. Calls are independent.
5. If Kira gets to play, she will score points at a rate of 100,000 per hour.

Calculate the expected number of points Kira will score before she leaves.

Random POVs Vol3

The rain.

The metal is cold against my palm.
A degree colder than the
Pencil-scrawled sheet before me.
My equations danced across the page
Mocking me the entire time.
I raised my chin in defiance.

I made a mistake somewhere
But exactly where, I ain’t sure.
I chanted the Balducci assumptions again one by one
Praying, cursing and rebuking myself all the while.
I punched the numbers on the metal again.
Midway, I could foresee a 3-digit difference.
I stopped, closed my eyes for a minute
And looked outside.
It is getting darker.

I am distracted, this you hinted one time.
I suddenly had the urge to call you.
Whew.
The rain pounded heavily on the roof.
And lightning sliced the sky.
I knew I am done for the day.
But the call has to wait.

A Birthday Song.

I wish you all the best life has to offer.
I wish you happiness and abundance.
I wish for the realization of your dreams.
I wish you a great career and a wonderful family.
I wish that your ideals may not fail you.

In moments of challenges…
Take courage from the truth and inspiration from love.
And more importantly, rejoice!

In times of discouragement…
Remember us, the people whose lives you have touched.
Then, rejoice!

In times of persecution and discrimination…
Remember that the spirit of a warrior can never be broken whilst
The genius of the man can never be overpowered;
That what they say doesn’t matter as much as what you say to yourself,
And that they are only inggit , duh!
And, rejoice! Remember that we postulate that we are beautiful!

In times of solitude…
Have faith that we are always there to share your loneliness and pain,
That we are just a click of a mouse away.
Still, rejoice! For it is in times of solitude that we hear our hearts speak.

In times of achievement and glory…
Believe us when we say, we never doubted you,
That credit eventually fell where it is due;
That we celebrate with you your triumph and happiness,
With champagne or beer, and grins plastered on our faces.
And more so, rejoice!

Happy Birthday, MaFia!

Random POVs Vol2

The coffee.

The third time I read the sentence
I knew it was futile.
My eyes hurt as much as my brain.
I looked at you again.

Even against the darkness,
I noticed the slight crease of your brows
And the mirth on your lips
As you read through the lines.

You paused, looked back
And typed furiously.
I flipped the magazine in my hands.
Funny, I can’t remember what her name is
But I know she gets paid 5000 an hour.
Numbers do really amaze me more than words.

My gaze went back to you again.
The fifth in ten minutes.
I am grateful that Shang has a joke for a generator
This way I get to observe you as boldly as I can.

I saw you squint at the page.
You used to do that when you were thinking.
Now, it could be the light.
Silently, I wondered
What else changed in 5 years?

I traced the contours of your face with my eyes
My gaze lingered at your lips.
You still are beautiful.
I emptied what’s left of my cup
And hoped that that went unnoticed.

I raised my eyes again
Only to find amusement in yours.
Uh-oh, busted.

Random POVs Vol1

The wait.

The cursor stares back at me.
Sigh.
This ain’t easy for me too,
I shouted back more for me against its angry glare.
I wonder why it is so stubborn
For when you think about it
This is confusing me a lot more.

5 minutes passed
And I can’t write a single word.
Surely, I should have forgotten, right?
Wrong.
It was 5 years now
But the pain is as fresh as newly-cut wound.
Now, why is this a good idea again?
Indeed, this is confusing me a lot more.

Just 5 minutes more
And I ready myself to bolt out the door.
I wonder why I would have to brave this wait
Not when I need to be just scared shitless.
The cursor blinks back again
And I stared just as angrily.
I finished my tea
And stood.
Maybe there won’t be any words coming…

5 steps.
A “hi” then a smile.
Thank heavens, I am wrong.