Yet another installment of puzzles...

[mendhak]

For a hot dog as the prize, what is the next number in this series?

341 444 533 602 705 848 1003 1098 1273 1420 .....


I'll give hints if you REALLY need it, and NO peeking!!


And here's another one for a hot dog AND a piece of NoteMe's ear:

My Dad has a miniature Pyramid of Egypt. It is 4 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/ 3) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.

[Simon Caiger]

If I'd known that there was a real frog on this forum, I'd have thought twice before being so cruel as to offer frogs legs as a prize.

Sorry Mendhak, trouble is it is so difficult not to offend anbody in some way these days.

Do you know if there is a jar of dill pickles posting on this forum as I am thinking of offering that as the next puzzle prize?

[Simon Caiger]

The pyramid will be 6.46 inches high.

Still working on the number series.

[mendhak]

Originally posted by Simon Caiger
The pyramid will be 6.46 inches high.

Sorry doggy... that's the wrong answer. Please show your work here too.

Oh and you better be the first to come up with the answer... wouldn't want to heat you up and sandwich you between two buns

Oh and there is a single dill pickle that does post on these forums, though the name escapes me. How about offering chopped up pieces of OrdinaryGuy as the next prize?

[mendhak]

Take note, (Simon), I've changed the numbers. I've made it much easier after I received a reprimanding from a friend of mine.

Now it's easy. Very VERY easy.

[Simon Caiger]

Thanks for the clue.

Next number in series is 1533.
Would have helped if you had posted the beginning of the series

The pyramid is 5.77 inches high

[mendhak]

Originally posted by Simon Caiger
Thanks for the clue.

Next number in series is 1533.
Would have helped if you had posted the beginning of the series

Impressive.

You're still off on the pyramid puzzle. Show your work.

[Simon Caiger]

Mass = Density * Volume

The mass of the miniature pyramid is to be the same as that of the new model so the density is inversely proportional to the volume.

For similar solid objects, the volume is proportional to the cube of the heights.

ie VolumeofNew/VolumeofOld = (HeightofNew/HeightofOld)^3

So we have :

HeightofNew = HeightofOld * (DensityofOld/DensityofNew)^1/3

HeightofNew = 4 * (3^1/3) = 5.77 inches


Errrr .... I think

[Simon Caiger]

Would you like some nicotine gum ?

I quit smoking 3 months ago.

Trouble is, I'm addicted to the gum now

[honeybee]

Originally posted by Simon Caiger
If I'd known that there was a real frog on this forum, I'd have thought twice before being so cruel as to offer frogs legs as a prize.

I guess the only trouble then would be you wouldn't have anybody trying. I mean who wants a frog's legs as a prize? Or NoteMe's earpiece (or piece of ear, whatever)?

Sorry, Mendhak, if you can put up something better for a prize, I am willing to consider giving it a try.
































And don't think it's just an excuse for hiding my inability at maths. It is.

.

[Simon Caiger]

I think some of our French friends would be delighted with a bag of frog's legs as a prize.

[mendhak]

Originally posted by Simon Caiger
Mass = Density * Volume

The mass of the miniature pyramid is to be the same as that of the new model so the density is inversely proportional to the volume.

For similar solid objects, the volume is proportional to the cube of the heights.

ie VolumeofNew/VolumeofOld = (HeightofNew/HeightofOld)^3

So we have :

HeightofNew = HeightofOld * (DensityofOld/DensityofNew)^1/3

HeightofNew = 4 * (3^1/3) = 5.77 inches


Errrr .... I think

OK... you're on the right track. You went wrong at the end.

[mendhak]

Honeybee, would you like a cigarette?

Simon... click the image in my sig. You quit smoking, wrong move man.

[Simon Caiger]

My big brother says that it's thr right answer








OK

[Simon Caiger]

Mendhak,

Interesting debate on that thread.

I'm not about to become one of those ex-smokers that goes around criticising and wafting smoke away from their face whenever a smoker comes within ten feet.

I used to choose to smoke, now I choose not to smoke.

By the way, I've chosen not to smoke on and off for the last 30 years

[mendhak]

Time's up, I guess. Here's the solution to the pyramid problem:



Mass = Density x Volume

Volume New / Volume Old = (H New / H Old) ^3.


In the above equation, H is the characteristic dimension (say, height).

If the mass is to be the same, then density is inversely proportional to volume. Also, the volumes are directly proportional to the cubes of the heights for objects that are geometrically similar. Therefore, the heights are seen to be inversely proportional to the cube roots of the densities. Thus,

Height New = Height Old x (Density old / Density New)^(1/3)

Height of model = 4 x [ 9^(1/3) ]

Which makes 8.32 inches.




As for the number series,
341 444 533 602 705 848 1003 1098 1273 1420 .....

If you take the 11th prime, and multiply it by its position, you get 341. The 12th prime into its position gives 444... and so on, until you get 1533.


OK, I get a hot dog now

[honeybee]

Originally posted by mendhak
Honeybee, would you like a cigarette?

Only if it's not prepared from seven butts. I prefer human butts to the cigarette ones

.

[Simon Caiger]

Mendhak,
I thought the pyramid was to be 1/3 the density, not 1/9 ??

[honeybee]

Originally posted by mendhak
OK, I get a hot dog now

Weird frog

.