h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

That's the correct answer. My model answer was as follows:

***

The easiest way to work this out is to consider their respective work rates.

In one hour, Barry and Gary can plaster 5 walls, Gary and Harry can plaster 3 walls, and Barry and Harry can plaster 4 walls.

Add these up, and in one hour you have 2 Barrys, 2 Garys and 2 Harrys plastering 5 + 3 + 4 = 12 walls.

So it follows that if they worked together, 1 Barry, 1 Gary and 1 Harry could plaster half as much, ie 6 walls in one hour. So they could plaster one wall in 60/6 or 10 minutes (the answer to part b)

Now if Barry and Gary can plaster 5 walls in an hour, and Barry, Gary and Harry can plaster 6 walls in an hour, then it follows that Harry is plastering only 1 wall in an hour, so it would take Harry one hour to plaster the wall on his own (the answer to part a)

So the solution is:

a) 1 hour
b) 10 minutes

***

On a sunny suburban street it is possible to find two neighbouring houses with an interesting property. The square number of one house number is the triangluar number of the neighouring house number.

What are the house numbers?

And, if you looked a little further on the other side of the street you may find the same properties effecting a couple of houses that are a few doors apart.

What are their house numbers also?


Geggs

Can you explain to me what a triangular number is? Any number multiplied by three? Or is it x³?

I was waiting for someone to ask.

Picture the triangle of red balls on a snooker table. A triangle with 1 row would contain 1 ball. A triangle with 2 rows has 3 balls. A 3 row triangle has 6 balls. A 4 row triangle has 10 balls, and the full 5 row snooker triangle has 15 balls.

Numerically, you sum the natural numbers up to the number you are considering. So the triangular number of 5 is 1+2+3+4+5=15, as we just saw on the snooker table.

Hope that's clear enough.


Geggs

Does the street have odd numbers on one side and even numbers on the other side?

It does indeed.


Geggs

Just popping in...

Looks like house numbers 6 & 8 and 35 & 49

Spot on! For extra points, could you give me the next pair of numbers with this property?

Either way, it Rudest Elf for the next question!


Geggs

Erm... sorry, but I'm away on holiday and won't have time.

Perhaps you can supply the next teaser.

But then I'll have to think of one!

Okay, I will. But I'll wait for an answer to the extension question first.


Geggs

Have we had 3 light bulbs puzzle yet, by the way?

If not, I'll do that one next.


Geggs

Hi Geggs,

It's 204/288.

Who's next?

Quite right. Well done.

I've always felt that to be an interesting little puzzle. Obviously, you could carry on hunting down more pairs the have the property, but the gaps between the numbers get bigger, and it takes increasing longer to reach each pair.

I once built a spreadsheet with the natural numbers in the first column, their triangle numbers in the next column, the roots of the triangle numbers in the next column, and finally a flag column showing whether the roots and natural numbers. In the whole spreadsheet (65 thousand odd rows) there were only a handful of pairs.

Kind of like the distribution of perfect numbers - you find the first one so easily you assume there must be loads, but they are actually fairly elusive.

Rudest Elf has declined to set the next one as they are on holiday. You can if you like, Icy.


Geggs

OK, an easy one, then:

How do you arrange six matchsticks to make four equilateral triangles?

Make a triangle with 3 matches. Then place the others on each corner of that triangle so that they stand up, one end touching each corner and the other ends of those matches meeting at the top of the triangle.
Much harder to explain than to do.

Absolutely correct, CD.

The shape is a tetrahedron, or triangular-based pyramid

Over to you...

Go ahead and post another please. I will be away on holiday soon.

I'll post one tomorrow (if nobody else does first)

Have a great holiday, CD

I guess I will, in time, become accustomed to the use of 'they' for he/she - as I have with 'their' for his/hers (No Problem! ) - but right now the 'they' construction still causes me some discomfort .

Actually, I'm a boy - not exactly a young one either - so you may refer to me as 'he'.......... but please not as 'Old Boy'.

Is it tomorrow already?

OK, a new one.

There are only three houses in my street and I live at number 2. If I add up all the house numbers up to and including mine, then the sum (1 + 2 = 3) is exactly half the number I get if I add up all the house numbers in the whole street (1 + 2 + 3 = 6).

I was so amazed that I told my friends at the pub. Well, they mercilessly took the mickey, but then they did the calculation and found it worked for them too.

We all live at different house numbers, so which are the numbers of my friends' houses?