Brain Teasers are Back!

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I asked Mrs R in case there was some fancy mathematical method that I didn’t know about. No such luck, so she also used first principles. She used ground distance covered as her frame of reference whereas my approach was to use relative airspeeds. Equivalent but different perspectives.

She noted that the faster aeroplane (we don’t call them airplanes in this household) had to travel 150ft plus an extra amount E being the distance the slower aeroplane has travelled. This gives (150+E)/1=A.

In the opposite direction it is (-150+E/3)/(1/3)=-A

She also concluded speeds of 300ft/s and 150ft/s.

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4281

Nice alternative approach.

4282

Wow ! that is tall !!

I lived in the Trucial States for about three years. It’s now called the UAE (Emirates). During a recent visit, we enjoyed a view from high up on the Burj Khalifa. Such a building hadn’t been imagined during the above three years. At approximately 830m it’s the tallest building in the world.

I’m confident that its absolutely perpendicular – well, for the purpose of this teaser !

Also, for the purpose of the teaser, lets assume the Earth is a perfect sphere, circumference 40,000km and the Burj Khalifa is 830m tall, from the earth’s surface to the tip of the antenna.

Assume an identical tower is constructed one kilometre north of the Burj Khalifa. Both towers are perpendicular, ie they each project along an extended Earth radial.

Clearly, the two towers are not parallel to each other. How much further apart are the tips of the antennae than the centres of the two tower bases.

(let’s ignore sway due to wind etc, etc..)

4283

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Hi everyone. I have these fabric tiles and need a way to arrange them so it looks more aesthetically pleasing. Can you help me ?
Thankyou.

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4284

How many do you have? Is it just the 16 small squares or is that just a sample of a much larger area?

4285

Mrs R came up with a fairly simple solution which I agree with.

However, I pointed out that her answer was not exact and I had a method that would give a slightly smaller answer that is exact.

When I did the calculation, it really was very close to Mrs R’s answer. We concluded that I was splitting hairs, quite literally!

4286

Yes just the 16. Thankyou

4287

You have 6 light, 5 medium and 5 dark squares.

Mrs R suggests using a diagonal pattern. She (a mathematician) used numbers of course. Something like:

1 2 3 1
3 1 2 3
2 3 1 2
1 2 3 1

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4288

I like it. :+1:

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4291

Mrs R gave an answer of just over 13cm.

My answer is very very slightly less.

4292

Well Ravvie ( and Mrs R), it seems to me that only we three have shown any interest in the concept of “perpendicular” and whether skyscrapers lean away from one another or not.

When I drafted my teaser, I simply had in mind the idea of scratching the old grey cells as to how we might define ‘perpendicular’ and the ‘order of magnitude’ by which very tall buildings across a city might diverge from ground floor to roof.

I picked ‘round’ numbers eg 40,000 km and 1km to keep things simple and I picked the Burj Khalifa at 830m so that the odd millimetre in the answer wouldn’t matter .

Now, you are talking about yourself and Mrs D splitting hairs - literally !! … I can think of better ways to spend an evening together :smiling_face_with_sunglasses:

Anyway, the best ‘exact’ answer that I can produce at the moment is 83 x Pi/2.

This approximates to 130mm (just over) depending on how accurately you specify Pi.

4293

I like both yours and Ravvie’s …depending on which way I look at them. :smiling_face_with_sunglasses:

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4294

If one of them looks in a mirror, it will see the other :grinning_face:

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4295

A project I am currently working on is to determine a new way to calculate π and other mathematical constants to an unnecessarily large precision. Actually it’s a way of turbocharging the fastest existing methods rather than being a totally different method. Yes, there are probably better ways of spending my time!

The teaser specified perfect assumptions, so I took this literally.

Mrs R’s solution was the same as yours. It measures the difference between the 1km on the Earth’s curved surface and that of a corresponding curve at an altitude of 830m. I suppose it is “as the crow flies” though.

My method measures the straight line distances between the two buildings at the top and bottom, say if measured by a laser.

When I worked out the answer it was almost a case of splitting the atom rather than splitting hairs. My answer is less than yours by slightly more than the diameter of a hydrogen atom!

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4296

Nice piece of work there Ravvie, Nice.

4297

With Xmas on the horizon, I thought a neat little party trick might be in order ! Well, I thought it was neat :smiling_face_with_sunglasses:

Blindfold Coins

Start with (say) 10 coins on a flat table or tray, all Heads-up ( the trick will work with any number of coins).

You, (the magician) are blindfolded. Your audience shuffles the coins and turns over as few or as many coins as they please. There will now be a mix of Heads and Tails, or possibly all Heads or even all Tails. (You are blindfold, so at the moment you don’t know the coin distribution).

You ask your audience to declare how many Tails-up coins there are. Let’s say “Four”

You now volunteer to divide the collection of coins (10 in this case) into two sets, each with the same number of Tails-up showing !! ….. How ?

You select four coins at random, without turning them over (remember, you are blindfold) and these coins form one of the two sets. The other six coins form the other set.

You (still blindfold) now turn over all four of the coins that you selected to create that first set.

There will be the same number of Tails-up coins in the first set of four as there are in the set of six.

You can remove the blindfold and bask in the inevitable applause !!!

As I said above, this works, regardless of the number of coins at the start.

PS I should add, the reason you pick four coins at random, is because the audience told you that there were four Tails-up coins. Ie, you always create that first set using the same number of coins as the audience declares to be Tails-up.

You might need to practice a little until you reach the standard of Tommy Cooper !

4298

Welsh Invasion!

Over dinner last night I pointed out to Mrs R that there were three Welsh teams in the English Football League Cup, that had reached this week’s Round of 16.

I then noted that two of them had been drawn to play each other.

“What are the chances of that?” Mrs R asked.

Unusually for us, I resorted to using Mathematics whilst Mrs R went for a lateral thinking approach. We did reach the same answer though.

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We are back and forth at the moment, so its more lateral thinking from time to time. The maths will have to wait a while.

Nice teaser Ravvie.

4300

Ok.

Despite still being back and forth on the move, I have tried to visualise the situation during the draw. By ‘visualize’ i mean I have a vague matrix in my mind.

I keep coming up with a 1 in 40 chance of two Welsh teams being drawn together.