Monday, November 10, 2014

The Challenge of the Shoe Seller

A shoe seller bought shoes from his supplier at a cost of RM21 per pair. He then put a price tag on them at RM29 per pair, intending to make a profit of RM8 per pair (ignoring other costs). A customer walked into his shop and bought a pair, and paid him with a RM50 note. However, the shoe seller had no small change. He therefore instructed his employee to go to the neighbouring shop to break the RM50 note. After breaking the RM50 into smaller notes, he wrapped up the pair of shoes and included the change of RM21 to his customer.

A few hours later, the neighbouring shop keeper came to inform the shoe seller that the RM50 note he exchanged earlier was actually fake money. In the end, the shoe seller had to pay RM50 back to his neighbour. Obviously, instead of making a profit from the transaction, the shoe seller actually suffered a loss. But how much did he lose?

Such was the question raised by my running buddy, Dr Peter Ong, during one of our long runs over a weekend sometime ago. We talk a great deal when we run together. Or rather, I talk a great deal, while he listens. The question isn't an impossibly tough one, but it provokes the mind to think. Now I have always said that these days our education system no longer teaches our children to think; it teaches the kids how to score straight "A"s, of course, but that doesn't really require them to think.

This morning, I chaired another one of our Monday meetings at the office. I was sharing my view that an approximate two thirds of the students in our universities are female and if it's not already the case right now, I'm expecting that similar proportions between the two genders can be seen in the job market too. 

However—and this is the point I'm trying to make—in the end, the top positions will almost always be dominated by men. I'm fully aware, of course, that the world has seen a number of female leaders such as Margeret Thatcher and Gloria Macapagal-Arroyo and the likes. But when seen as a whole, the top positions are overwhelmingly male. Why is that so?

Women are extremely good when deliberating detailed matters, especially from the theoretical point of view. They are sharp and meticulous and willing to swim in the abstract, turning every single issue down to the micro and atomic levels. Their solutions are very often impeccable and deserve an "A" for the university exams. However, these solutions are not always practical, and may not always reflect what's going on around us. Many ordinary problems in this world require simple solutions derived from common sense approach; not complicated mind boggling calculations based on bombastic formulas. It is in that sense that, in my opinion, men can quite naturally outdo women. This is speaking from general observation of course.

I meant to prove my point in the meeting this morning, and I threw out the above question to the audience. They ranged from high school to university education. There were 5 males and 6 females in the audience; so it was about balance. I told them to write down their answers on a piece of paper, and then those were to be submitted to me. I had expected that not all of them would be able to find the answer (maths is almost everybody's weakness), but I reckoned that the guys would certainly do better than the gals.

Well, what d'you know, all of them failed to get the answer—even after several tries! Not only have I failed to prove my point through this little experiment, but I have also discovered that none of my staff had what it takes to be in the shoe business!


Peng Aun said...

A very interesting Mathematical question. Could you please kindly provide the correct answer? My colleagues and I cannot agree on a common answer. Thank you.

Cornelius said...

Hi Peng Aun,

Thanks for visiting my blog, and thanks for your comment. Before I reveal the answer, however, I'd like to clarify one point. For the purpose of THIS question, we are ignoring other inherent costs in running the business, e.g. shop rental, telephone and electricity, employee's salaries etc. We are looking strictly at the cost of the shoes, the supposed profit margin from the transaction, and the effect of involving the neighbouring shop keeping with the fake RM50 note.

The reason I'm bringing this up is because SOME women try very hard to be overly detailed in their calculations and would like to take into account EVERYTHING in their attempt to arrive at the "correct" solution, but very often miss the whole picture by a huge margin.

Ignore all those other costs, and see if you could agree on a common answer. I'll elaborate further later during lunch break.

Peng Aun said...

Hi Cornelius,

We do not take into calculations all the other inherent costs. However, our answers are RM42, RM84 and RM92. Please kindly help us to solve our disputation. Thank you.

Cornelius said...

The problem with this sort of question is that it sort of forces the solver to focus on the small elements, but ignore the big picture!

But when seeing the problem from a distance, what we see is actually a scenario of 2 separate transactions:

(1) Shoe seller and his neighbour;

(2) Shoe seller and his customer

Never mind all those nitty gritty elements in between which are there just to confuse the mind. Let's remain true to the "real" issues!

Now to deal with (1) above first, and ignoring the nitty gritty, when we look at it from a distance, what we see is actually, the shoe seller gave a fake RM50 note to his neighbour in return for RM50 smaller change of REAL money. That is a gain of RM50! However, at the end of the story, he had to pay back RM50 of REAL money to his neighbour. What does that tell us? It tells us that the shoe seller incurred neither gain nor loss as far as his dealing with his neighbour is concerned. Net position is ZERO.

OK, now that (1) is out of the picture, we are better able to see (2) clearly. If there is any gain or loss, it is there that we should find it! And here, it is much simpler. Shoe seller lost a pair of shoes at the cost of RM21 (paid to his supplier); plus the RM21 cash that he gave the buyer (supposedly as change for his RM50 note, which turned out to be fake). Therefore the total amount lost is RM21 + RM21 = RM42.

Well done to those who found RM42.

Many of the problems in this world can be solved with common sense and looking at the whole picture. But many people just spend their resources focusing on the nitty gritty and confusing themselves in the process.

Peng Aun said...

Hi Cornelius,
Thank you very much for the well-explained answer. I agree 100% with your last paragraph. Looking forward to your next posting in your blog which I read every week. All the best wishes to you.

bk said...

The shoes was paid for. How did the seller lost on this?
He took out only RM50 to pay his neighbour. Transaction with the buyer was done accordingly, only that the Rm50 was fake.

Cornelius said...

Thanks, bk, for your comment/question. I'm trying to fathom where you're coming from, but if I understood you correctly, you're saying that you consider payment with FAKE money is as good as payment with REAL money, is that right? OK, let me try to respond.

"The shoes was paid for. How did the seller lost on this?"

No, not exactly. If for example you sell a book to me and I "pay" you with Monopoly money, would you say that the book is already "paid for"? Well, I see it differently; and I'm confident that it's the most natural way of seeing it. When the buyer "paid" with fake money, that is not actually "paying" in the true sense of the word, because he is "paying" with a worthless paper. The shoe seller received a piece of paper worth ZERO, so whatever the buyer walked away with, that must be deemed as losses to the seller (since the seller didn't get anything except for a piece of worthless paper).

In return for a piece of worthless paper, the seller gave away a pair of shoes which he paid RM21 to his supplier; as well as giving away RM21 cash (supposed to have been the buyer's change). That is a total loss worth RM42 (in cash and merchandise).

As for the neighbour, the shoe seller got RM50 of real money from him, but later he had to pay back the same amount of real money. So that is even, i.e. net position is ZERO; no gain, no loss.

Cornelius said...

Oh! I meant to respond to Peng Aun, but I forgot and went straight to responding to bk instead!

Thanks, Peng Aun, for being a regular reader of this blog. I hope my posts will continue to interest you!

Cornelius said...

I'm still getting messages from friends about this question. They're still unhappy with my solution and explanation because to them I've been rather reckless with the way how I've ignored the nitty gritty details of the story. I suppose my method is not up to the standard of what's required in school. Therefore, I've decided to explain the solution yet again, but this time by adopting the standard school exams approach. So her goes nothing!

We start with the RM50 fake money from the buyer. This is exchanged with the shoe seller's neighbour with real money in smaller denominations. So now, with the real money, the shoe seller proceeds with the transaction with his customer.

RM50 less RM21 for the buyer's change = RM29


RM29 less RM21 capital cost of shoes (paid to supplier) = RM8

Meaning that the shoe seller at this point has made a profit of RM8 like he's supposed to. That is a gain (positive) of RM8. That's the end of the transaction with his customer.

But now comes the revelation of the fake RM50 note, and the shoe seller has to pay back RM50 to his neighbour.

He pays RM50 of real money to his neighbour. That is a loss (negative). But that is partially offset by the RM8 profit (positive) that he made earlier. Mathematically, we can count like this:

RM8 - RM50 = - RM42

We still get the same result, i.e. a loss (negative) of RM42. As you can see, this method is more complicated than my reckless approach. But I hope it will make my friends happier.