Mental Nuts-- Can You Crack 'em?

[ZenGum]

Originally Posted by HungLikeJesus

But that's only $7.50 per acre! Now I have to figure out how to go back to 1921 to buy some land.

Be sure to take 1,000 3/4 cent pieces with you.

[BigV]

Originally Posted by ZenGum

There is a trap in the question - that we might mistake "one-half mile square" for half a square mile, when of course a square half a mile on each side is a quarter of a square mile.

Glatt was way too smart for that. Pfft.

ETA, For this New Years Eve, I'd like to meet a girl as easy as this puzzle.

eta: usually, if you can find that button, it's pretty easy from there.

[infinite monkey]

Do I have to give back my trophy?

[Rhianne]

Originally Posted by infinite monkey

Do I have to give back my trophy?

You got a trophy? I'm still waiting for the free circus ticket I was told I'd receive for getting the first one right.

[infinite monkey]

But Rhianne, y'are at the circus, y'are! It's called "The Cellar"

[Rhianne]

There's no shortage of clowns, that's for sure!

[infinite monkey]

Send in me, there's got to be me [/judycollins]

[footfootfoot]

Here is nut # 10 which is more of an origami thing. I suppose for some people this sort of thing is a challenge.

I am also putting up #11, a proper mental nut.

And Rhianne, I forgot to mention shipping and handling and a 2.5% ticketmaster surcharge is not included in that free ticket.

[HungLikeJesus]

I'm not sure I get the question, but I'll guess the answer is 128.

If the answer can be a fraction, then it should be 4.766.

[footfootfoot]

Originally Posted by HungLikeJesus

I'm not sure I get the question, but I'll guess the answer is 128.

That may be the answer to #10, but not #11.

I think the question is asking if you had a cube made of cubic blocks (the size is irrelevant as long as they are all the same size cubes) and you surrounded the cube with more of the same sized blocks, so that the same number of blocks were in the large cube as in the surrounding square, how many cubic blocks would you have?

[HungLikeJesus]

I was thinking what number has a square root and a cube root that are both whole numbers. That's where I came up with 128.

If the square has to be touching the cube, the answer would be 4.766.

If the square could be much larger than the cube, than there could be many answers.

Edit: I'm re-thinking this.

[footfootfoot]

Well that's not the answer either and I can't really figure out how they got the answer they did.

[ZenGum]

Okay, the stuff about pumpkin seeds is distraction.

I want to start by understanding the question. Here are some clear points for starters:

1. We take blocks of a regular size, 1x1x1.
2. We arrange some into a perfect cube.
3. We arrange others into a perfect square. *see post 105
4. The number of blocks used to make the cube must be equal to the number of blocks used to make the square.
5. Adding these numbers together is the final answer.
6. The cube must be able to fit inside the square.

Now for some less certain parts of the question:
7. There is exactly one correct answer.
8. This must be an integer.

Now for some assumptions which are not stipulated. The solution probably lies in challenging one or more of these:
9. The square must touch the cube at at least one point.
10. The square must abut the cube along all of the cube's faces.
11. The square is only one layer high.
12. The square is only one layer thick.
13. The square is on the same alignment as the cube.

Violating 10 makes it fairly easy. You could have a cube 4x4x4, having 64 blocks, and make a square 16 blocks each side around it, thus using 16x4 = 64 blocks, thus reaching HLJ's answer of 128. Or you could make the square double height, 8 blocks per side, and still use 64 blocks. *see post 105

This does not deliver a uniquely correct answer, since other combinatiosn work with this.
You could have a cube of 6x6x6 = 216 blocks, and a square 8 blocks per side and 6 blocks high (8x4)x6 =216 blocks.

Or a cube 100x100x100 = 1,000,000 and a square 250 long and 1,000 high (250x4)x1000 = 1,000,000.

If you reject 10 and 13 you can play around with Pythagorean triads, but I had a look and couldn't find anything promising.

What the hell kind of pumpkin has cubic seeds, anyway?

[BigV]

Perhaps this pumpkin math fact will help:

Do you know the ratio between a pumpkin's circumference and a pumpkin's radius?








Pumpkin

[ZenGum]

3. We arrange others into a perfect square.

Violating 10 makes it fairly easy. You could have a cube 4x4x4, having 64 blocks, and make a square 16 blocks each side around it, thus using 16x4 = 64 blocks, thus reaching HLJ's answer of 128. Or you could make the square double height, 8 blocks per side, and still use 64 blocks.

If we keep 10 but tinker with 3 and define a square as a line formed by one edge of a row of blocks, we get another option.

Think of a cube 4x4x4. Then wall this in with a ring 4 cubes on each side, i.e. leave the corners unfilled. Make the ring four blocks high. The square is the inside edge of the outer lines of blocks.