Brain Teaser No 1

Don,

Your figure is almost an exact copy of mine (yours is a lot neater). Thanks for the help,

cheers

Dan

quote:

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Originally posted by Don Atkinson:
A Monumental Problem.

A 10 tonne statue with a flat bottom, has to be placed upon a pedestal by crane. There is no way of lifting the statue except by slings under the base.

How could you arrange to set the statue on the pedestal and get the slings out ?

Cheers

Don

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Still no solutions to this one, nothing springs to mind, anybody else got a clue?

Matthew

I posted

ice ice baby

some time ago

Matthew,

Dobbin said I posted ice ice baby some time ago
and I commented Cool answer man, cool answer.

Sorry it was all too subtle........

Just to remove the subtleness, a few suitable ice cubes, strategically placed on the plinth, statute lowered onto ice cube, slings withdrawn, ice cubes melt, little bit of panic as statute tilts slightly. and we're home and dry.......well, once the sun has dried the melted ice...

Cheers

Don

Dan,

p.s. so Don is 1/2 way the correct answer?

Sorry, didn't think to close this one out because both you and Matthew hit it hard.

But just to avoid doubt, 1/2 way was my view also..........

Unless someone else knows better....

Cheers

Don

another simple (in the head) one:

After peeling an orange, I notice all the segments are identical. I eat two segments and realise that I haven't change the area of the peeled orange at all. How many segments are left?

-Dan

six

The ice slipped me by!

Matthew

A clock consists of 12 small identical circular plates, numbered and seated on a circle so that each touches both its neighbours. The clock also has a wheel that runs around the outside of the clockface, has the same radius as each of the small plates, and has its centre attached by a rod and spring to the minute hand. The spring keeps tension on the wheel in the direction of the clock centre so that as the minute hand rotates the wheel rolls along the outer contours of the 12 plates without losing surface contact. How many times does the wheel rotate with respect to the clock centre each hour?

Matthew,

Six is correct.

I believe your wheel rotates 3 times.

-Dan

Ooooops,

Prompted by your post above, Lynn, i've just looked back at my 3/4/5 triangle drawing. Several times i have refered to 'similar' triangles when i really meant 'congruent' triangles.

100 times
I really meant congruent triangles
I really meant congruent triangles
I really meant congruent triangles
I really meant congruent tria.....

Cheers

Don

Dan,

I think you will need to revisit the problem.

Matthew

Matthew,
I reckon the wheel rotates 4 times.
Steve D

Nope

quote:

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How many times does the wheel rotate with respect to the clock centre each hour?

---

Once.

--J

So we're all agreed then?

The wheel rotates three times per hour; but with respect to the centre of the clock this is only once an hour.....

Well spotted Jeremy.
Dan, IMHO you're entitled to feel cheated. But as they say in all exams, you must read the question carefully. I'm sure Matthew will apologise....
Steve??????

Cheers

Don

quote:

---

The wheel rotates three times per hour

---

I thought it was four.

Three times from rubbing along the edges and once because the edges end up in a loop.

But probably not.

Paul

Nope, still wrong.

Matthew

Matthew,
Sorry about the duff maths earlier. What I meant to say is that the outside wheel will do 6 revolutions in 1 hour.
Try rolling a £1 coin round another £1 coin. The outside one actually does 2 revolutions.
Steve D

Steve,

Thats the correct answer.

Matthew

Phew! Glad that one is sorted.

Dan

I had this suspicion it looked a bit like a cuckoo clock.....

nicely sorted steved

Cheers

Don

Roots

This map shows the road layout where Janet and John live. How many different routes are there for them to cycle from home to school (together), never going northwards ?

Cheers

Don

Roots

First, label the successive nodes leading southwards between home and school a to h.

Then list the nodes reached by never-northward arcs from these nodes:

a -> b, c, e
b -> c, d
c -> d
d -> e, h
e -> f, g
f -> g, h
g -> h

Let n(xy) be the number of never-northward routes from x to y.

Then, using the above list:

n(gh) = 1
n(fh) = n(gh) + 1 = 2
n(eh) = n(fh) + n(gh) = 2 + 1 = 3
n(dh) = n(eh) + 1 = 3 + 1 = 4
n(ch) = n(dh) = 4
n(bh) = n(ch) + n(dh) = 4 + 4 = 8
n(ah) = n(bh) + n(ch) + n(eh) = 8 + 4 + 3 = 15

--J

JerremyD,

You're absolutely right and quite a neat explanation.

I thought I'd wait a while to see if there were any challengers, but none!

My solution ismuch more pedestrian (dreadful pun)

I labled allthe nodes, even those with just one route in and one route out.

Then I drew a tree (bit like a fault tree or probability tree) which branched whenever there was more than one route out.

The diagrams below should help

Cheers

Don

And the tree diagram

Cheers

Don