# Brain Teasers are Back!

Yep, that’s what I recon as well. Preston train arrives say, 6 minutes before the Blackpool train and we have an hourly service, 9 times out of ten the Preston train will be the first to arrive.

3 minutes and a half hour service would be similar etc…

Nice solution JR and nice teaser Steve.

For anyone who has tried the ‘Road from X to Y’ puzzle that I set a couple of days ago, here is my solution.

Yes, correct answer to the train puzzle from Don and others. It’s an obvious solution but I have to admit I didn’t get it the first time I saw the puzzle.

Same here. I had visions of either a ‘Loop’ somewhere in the system or a rapidly increasing number of trains forming a railway museum in Blackpool !!

If you’ve got a bit of time on your hands …

As I draft this teaser, the time on my analogue watch shows half past one.

What is the angle between the hour hand and the minute hand ?

School Parents Evening

My daughter went to a parents’ evening last night at her local school.

She said there were twice as many parents as children and twice as many children as teachers.

The meeting room was full to its capacity of 35.

How many children, parents and teachers were there ?

My mental arithmetic suggests 135 degrees for the angle, and 10, 20, 5 for children, parents, teachers.

nothing wrong with your mental arithmetic Steve. Well done on both counts.

Flashing Lights.

Now that spring and gardening are in the air, Mrs D bought three identical sets of garden lights (strings of LED lights) to adorn the two garden arches and the gazebo.

Each set of lights has eight possible settings which are automatically selected at random, with equal probability, when switched-on. They are connected to the same extension system so all come on together, but the random settings are independent.

One of the settings provides a steady set of lights. Each of the other seven settings provides some sequence of flashing lights.

What is the probability that at least one set of lights will be flashing each time the three sets are switched on ?

Hint.
What is the probability of all three LED strings being steady ?

No takers so I’ll have a go:

Probability of at least one set flashing is 511/512. (Approx 99.8%)

In other words, P = 1 - (1/8 * 1/8 * 1/8)

The remaining 512th (approx 0.2%) is the probability that they are all steady when switched on.

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Well done Bobby. And very neatly explained.

Mrs D needed a bit more persuasion when I gave her the answer. So, just in case it also helps others, here is how I explained this one to her ….

… The first string of lights could take up any one of 8 modes. (one steady, seven flashing)

For each one of these eight modes, the second string of lights could also take up any one of eight modes, giving a total so far, of 8 * 8 = 64 possible modes.

Likewise, for each of these 64 modes, the third string of lights could also take up any one of eight possible modes, giving a grand total of, 64 * 8 = 512 possible modes (ie 8 * 8 * 8 = 512)

Of these 512 possible modes, only one will produce Steady/Steady/Steady. Meaning that each and every one of the other 511 modes will incorporate at least one set of flashing lights.

Hence, the probability of at least one set of flashing lights is 511 out of 512 ie 511/512 = 0.998 or 99.8% (approx.)

Likewise, the probability of getting no flashing lights, ie only three sets of steady lights, is 1 out of 512 ie 1/512 = 0.002 or 0.2% (approx.)

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In the English Language there is a word in which the first two letters signify a male, the first three letters signify a female, the first four letters describe a great man and the whole word a great woman.

What is that word ?

Took me a while, but got; heroine.

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Well done Mike.
Took me a while as well.
Back to Wordle, where you also do well

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Fireworks.

I have it on good authority, that on Coronation Day, there will be a fireworks display.

There will be five primary rockets which when lit, will rise into the sky as Red streaks (light trails). Each one will then split into 11 fireworks each emitting a White streak (light trail). Then finally, each of these will produce 18 Blue streaks (light trails).

How many light trails in total will this display comprise ?

Modern tech … eg smartphones !!

My smartphone has a 2.4GHz processor. I understand this means it can do 2400 million calculations in a second…

I want to download a new ‘app’ to this phone and that process will require the phone to do 1.8 x 10^11 calculations. (don’t ask me, i’m just reading the blurb)…

How many seconds will this download take ? I need the answer as an easy-to-understand ordinary number!

After a minute or so it will say 100%, but then it will whirl away for three hours until one finally gives up the will to live.

Or is that just me?

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1800/2.4 = 750 seconds.

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I think you’ve hit the nail on the head, so to speak, Ravvie.

Also you are not alone with the 3 hour follow-up …

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