So I made the booking. Then, like a good shopper, I kept checking other websites for lower rates. Turns out I was lucky: a couple weeks later, I found the exact same reservation on Priceline.com for $30 cheaper.

I quickly submitted a price matching claim and called up Hotels.com so they could confirm the lower rate and provide a refund. I thought I had followed all of their rules, and for extra evidence, I submitted a screenshot of the lower price.

And that’s where the fun begins. They confirmed the price, but then informed me I was not eligible for a refund. Huh?

Here’s what they explained to me, and how I was able to negotiate almost the same discount.

Hotels.com price matching guarantee

Here are the terms of the price matching guarantee:

Hotels.com reservations are guaranteed to be the lowest rate you can find. If there is a lower rate publicly available for the same dates and the same hotel or vacation rental and room category, you must contact us prior to the hotel’s cancellation deadline. Deadlines vary by hotel and travel dates. Please refer to your booking confirmation for the applicable deadline.

Bookings that cannot be cancelled are not subject to this guarantee.

If your booking qualifies for this guarantee, we will either, at our option, refund the difference to you, or, if you would prefer, allow you to cancel the reservation without penalty.

If you book a hotel that does not require payment at the time of booking, your Price Match Guarantee request will be refunded within 72 hours upon verification of your completed stay, once you have checked out of your hotel.

The policy seems generally fair: if you find a lower publicly available price on another site, they will match the price.

The catch

You have to read between the lines to see why the price matching guarantee does not offer much power.

It’s specifically the second condition: “Bookings that cannot be cancelled are not subject to this guarantee.”

Think about this more closely. Hotels.com is saying they will only price match on reservations that CAN be cancelled. But in that case, who cares about a price matching guarantee?

If the booking could be cancelled, I could just cancel it for free and then make a new booking at the lower price.

Hotels.com is basically saying they will price match on bookings that you on your own could have cancelled and gotten a lower price!

If, on the other hand, you actually paid them money up-front, and you found a lower price, then oh well, you are out of luck.

This is a pretty big catch in the price matching guarantee.

My story

So that’s the technicality that got me. My booking was a non-refundable reservation and thus not eligible for price matching.

I felt this was an absurd policy, so I immediately asked to speak to a manager to explain it.

The manager turned out to be helpful, probably because she had dealt with this issue before. To alleviate the situation, she quickly offered me a one-time courtesy 5 percent discount, which amounted to about the same amount as if I had gotten a full refund.

All in all, I will give the call center credit for quickly resolving the issue. After all, it’s not their fault that Hotels.com has such a quirky price matching policy.

(Perhaps it’s no surprise that Hotels.com is being sued over its price matching guarantee policy.)

In the end, the experience has made me hesitant to book non-refundable rates on Hotels.com and other websites as well with the weak assurance of a price match guarantee.

I’m largely going to stick with reservations that can be cancelled (so I can rebook if I find a lower price) or look for last minute deals.

Alice draws a line connecting two of the points with a line segment. Bob and Alice move in turn, but the line segment cannot cross any of the previously drawn lines.

A player who cannot draw a suitable line loses.

What’s the winning strategy and who has it?

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The answer

The problem is easier to analyze when considering smaller cases.

Suppose there are 4 points around a circle numbered in clockwise fashion 1, 2, 3, 4. Let’s say Alice draws a line between the points 1 and 3. The points 2 and 4 are separated on opposite sides of the line. Bob’s line would intersect Alice’s, and so Bob loses on his first turn.

If there are 6 points, then Alice should draw a line that connects points 1 and 4. Bob can then connect points 2 and 3, or 5 and 6. Either way, Alice can connect the points that Bob does not pick, and then Bob cannot draw any more lines so he loses.

It turns out this pattern continues, Alice can win with 100 points if she connects the points numbered 1 and 51 on her first turn–I’ll leave it to you to fill in the details

I wanted to have a get-together with some coworkers from a previous job. The problem was that I was unsure if the guests all got along.

I decided to do a simple test on Facebook. I personally was friends with each of the 5 people I wanted to invite.

But were each of them mutual friends with everyone too?

I went to person A’s profile and found he was in fact friends with the other guests B, C, D, and E.

The question is this: for a group of 5 people, what is the minimum number of profiles you have to check to make sure each person is a friend with everyone else? What about for n people?

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The answer

In a group of 2 people, you only have to check 1 person’s profile. If person A is friends with person B, then person B is necessarily friends with person A. In mathematical terms, the relation of mutual friends is “reflexive.”

Similarly, in a group of 3 people, you only need to check 2 people’s profiles. If person A is friends with B and C, and person B is friends with C as well, then person C is necessarily friends with A and B too.

We can generalize: in a group of n people, one needs to check n – 1 profiles. It is necessary to check the first n – 1 people’s friends’ lists to make sure each person is friends with each other and the last person in the group. But once that is verified, the last person must necessarily be friends with everyone else.

You can think about this graphically. Represent the group as a set of n points, and draw a line between points if the two people are friends. If the first n – 1 points are connected to every other point by a line, then the last point must also be connected to every other point (there are n – 1 degrees of freedom).

Thus, in a group of 5, one needs to check the friends list from 4 profiles.

The amusing part is the park is open from 5am until the unusual time of 12:01am.

This is evidently to avoid the confusion about noon and midnight:

The use of “12:00 midnight” or “midnight” is still problematic because it does not distinguish between the midnight at the start of a particular day and the midnight at its end. To avoid confusion and error, some U.S. style guides recommend either clarifying “midnight” with other context clues, or not referring to midnight at all. For an example of the latter method, “midnight” is replaced with “11:59 p.m.” for the end of a day or “12:01 a.m.” for the start of the next day. That has become common in the United States in legal contracts and for airplane, bus, or train schedules, though some schedules use other conventions

You can see an example of this at the Hertz car rental website. If you try to make a reservation for midnight, you get the following warning message:

This is all well and good, but it’s exactly the reason I tend to use the less problematic 24-hour time system.

My local grocer sells a variety of egg sizes. Can you figure out which one is cheapest?

Here are the prices:

Here is how I approached the problem.

Step 1: get the weights

To solve the problem, one needs to find the weights of the various sizes.

In my case, the weights were actually written on the egg cartons. But if they weren’t, I could have looked up the USDA regulations on egg sizes to find the following weights.

Step 2: compare unit costs

Now we can attack the problem. We will divide the cost by the weight to figure out the unit cost of each egg size.

It is clear from the table that eggs slightly decrease in unit cost the larger the size.

It’s not a big change: the jumbo sized eggs are roughly 3 percent cheaper than the medium sized ones. Still, this value adds up because I buy eggs almost every week.

Step 3: consider yolk:white ratio

There is one extra consideration. The unit cost is the appropriate measure if I were eating the entire egg.

But clearly I am going to throw away the shell. And as is the case, I typically throw the yolk away and just eat the whites.

If the extra weight from the larger eggs were due to the increased shell size or yolk size, then the larger sized eggs would not make sense.

So the question is: do the larger eggs contain more egg whites to make it worth it?

(Incidentally, buying eggs and throwing away the yolk is also a lot cheaper than buying products that only contain egg whites)

I did a bit of searching and luckily found a research paper on exactly this topic of the ratio of egg yolks and whites–it’s amazing the amount of information out there.

It turns out that the weight of the contents in an egg are proportional to its size. As a general rule of thumb, an egg’s weight is roughly 11 percent due to its shell, 31 percent from its yolk, and 58 percent from the white.

This means that egg white will increase proportionally with the egg’s size, and so the jumbo eggs are still the cheapest in unit cost.

Here are the numbers to confirm that jumbo eggs are still cheapest in terms of an egg-white only basis.

Conclusion

At these prices, it’s best for me to buy the jumbo eggs.

In general, one can compare the unit cost of egg sizes to figure out the best deal. This is true even if you care only about the egg whites or yolks, because both typically increase proportionally with egg size.