Math puzzle

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Denis said:
energy equals mass times the speed of light SQUARED (arranged as a square) :idea:
Click to expand...

?Yeah, but I'm thinking that only "THESPEEDOFLIGHT" should be "squared".

Kapish ? :wink:



?
 
But there are no grouping symbols - so only last term gets squared (in this case T).
 
The cleverness of my Dingbat Puzzle is apparently too much for you 2 inferiors to comprehend :wink:
 
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TchrWill said:
Thats 8.
Click to expand...

I think that I got it, and the forced spacials hurt. (I did not immediately realize that my first two cuts result in six pieces, instead of three. I had to draw a picture.)

Make two "sideways" cuts, but angle them like intersecting planes. Then cut the six pieces in half.

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[attachment=0:31xxqcax]Breakfast.JPG[/attachment:31xxqcax]

MY EDIT: It just occurred to me that Denis was probably thinking "one sideways cut followed by two angled cuts from above", despite what was typed. (Same idea; rotated bagel.)
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What's remarkable about this:

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11 + 2 = 12 + 1

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:?:



Code: 
    44.44
      ?


{I'M A DOT IN PLACE} EQUALS {A  'DECIMAL  POINT}
[/spoiler:2fqd5qwq]
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It's a ? UNIVERSE

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Code: 
     ?          THESP
                EEDOF
                LIGHT

     ×        M A S S

     E  Q  U  A  L  S

     E  N  E  R  G  Y

?
 
Re:

I think that I got it, and the forced spacials hurt. (I did not immediately realize that my first two cuts result in six pieces, instead of three. I had to draw a picture.)

Make two "sideways" cuts, but angle them like intersecting planes. Then cut the six pieces in half.

Thats 10, or I am clearly not understanding your picture.?

It just occurred to me that Denis was probably thinking "one sideways cut followed by two angled cuts from above", despite what was typed. (Same idea; rotated bagel.)

How can you slice a bagel into 12 pieces with only 3 cuts?

Initially, an interesting problem, but now, a piece of cake, or bagel.

Clearly, you can cut a bagel into 2 equal pieces with either 1 vertical slice or 1 horizontal slice, 1 cut.

Also, as clearly, you can cut a bagel into 4 equal pieces with 2 perpendicular slices through the center of the bagel, 2 cuts.

You can also cut the bagel into 4 equal pieces with 1 vertical cut and 1 horizontal cut, 2 cuts.

You can make one vertical cut tangent to the center hole, another vertical cut parallel to the first cut on the opposite side of the bagel hole and one horizontal cut through the whole bagel for 6 unequal pieces, 3 cuts.

You can make two perpendicular vertical cuts through the center and one horizontal cut to divide the bagel into 8 pieces, 3 cuts.

Okay, hold on to your hat.
You can make one vertical cut through the center and one horizontal cut through the thickness creating 4 equal quarter slices.
Take two of the slices (half the circle) and lay them atop the other two slices so that you see four pieces an top of one another appearing as half a bagel.
Now, the trick; place the knife tangent to the inner hole and parallel to the straight diameter slice of the four pieces.
Cut through all four pieces vertically and you will have 12, definitely unequal, pieces of bagel.
Since nothing was said about the pieces being of equal size, I think this meets the requirement.
With a bagel diameter of 4 inches and a center hole diameter of 1 inch, you end up with 8 pieces of .783 sq.in. each and 4 pieces of 4.304 sq.in. each.

If you can get your hands on a wedge shaped cutting tool with an apex angle of 60 degrees, you can cut through the half slices and create 12 equal pieces of 60 degrees each.

Enjoy.
 
Re:

Hello, mmm4444bot!

Got it!

Here's something else for Soroban and Denis.
Saw this in a Bahamas newspaper.

Code: 
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDWESTDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
Click to expand...

Drag cursor between te asterisks.

* West Indies (WEST in D's) *

 
Denis said:
West Indies : "west" in d's

One for you:
Code: 
E  N  E  R  G  Y
E  Q  U  A  L  S
M  A  S  S  T  I
M  E  S  T  H  E
S  P  E  E  D  O
F  L  I  G  H  T
Click to expand...
I already posted that as answer, Soroban.
 
?

Denis said:
a 3by5 is a square?
Click to expand...

Stop counting characters, and use your imagination, from a graphic-arts point-of-view. (Character manipulations are limited, here.)

?
 
\(\displaystyle Juicy \ Burger, \ in \ regards \ to \ mmm4444bot.'s \ poser, \ if \ we \ observe \ the \ great \ circle \ of \ a \ sphere\)

\(\displaystyle \ where \ R \ = \ radius \ of \ sphere, \ r \ = \ radius \ of \ the \ cylinder, \ and \ centered \ at \ origin, \ then \ we\)

\(\displaystyle \ have:\)

\(\displaystyle V_{remaining} \ = \ V_{sphere}-[V_{cylinder}+V_{caps}]\)

\(\displaystyle = \ \frac{4\pi R^{3}}{3}-\bigg[\pi r^{2}h+2\pi\int_{h/2}^{R}(R^{2}-y^{2})dy\bigg]\)

\(\displaystyle = \ \frac{4\pi R^{3}}{3}-\bigg[\pi h(R^{2}-h^{2}/4)+2\pi\int_{h/2}^{R}(R^{2}-y^{2})dy\bigg], \ r^{2} \ = \ R^{2}-h^{2}/4\)

\(\displaystyle Hence \ (with \ a \ little \ algebra), \ V \ of \ remaining \ sphere \ = \ \frac{\pi h^{3}}{6}. \ Note: \ The \ volume \ is\)

\(\displaystyle \ independent \ of\ R.\)

\(\displaystyle For \ example, \ when \ h \ = \ 6 \ units, \ we \ have:\)

\(\displaystyle V \ of \ remaining \ sphere \ = \ \frac{4\pi R^{3}}{3}-\bigg[6\pi(R^{2}-9)+2\pi\int_{3}^{R}(R^{2}-y^{2})dy\bigg]\)

\(\displaystyle = \ \frac{4\pi R^{3}}{3}-\bigg[6\pi R^{2}-54\pi+2\pi[R^{2}y-y^{3}/3]_{3}^{R}\bigg]\)

\(\displaystyle = \ \frac{4\pi R^{3}}{3}-\bigg[6\pi R^{2}-54\pi+\frac{4\pi R^{3}}{3}-6\pi R^{2}+18\pi\bigg]\)

\(\displaystyle = \ \frac{4\pi R^{3}}{3}-6\pi R^{2}+54\pi-\frac{4\pi R^{3}}{3}+6\pi R^{2}-18\pi \ = \ 36\pi \ cu. \ units.\)

\(\displaystyle However, \ to \ avoid \ all \ this \ grunt \ work, \ V \ = \ \frac{\pi6^{3}}{6} \ = \ 36\pi \ cu. \ units.\)

\(\displaystyle On \ the \ first \ page \ of \ this \ thread, \ I'm \ confused \ on \ TchrWill's \ volume \ of \ caps.\)
 
\(\displaystyle Speaking \ of \ polar \ bears \ (1st \ part \ of \ this \ thread), \ I \ wonder \ what \ would \ happen \ (over \ a \ long\)

\(\displaystyle \ time), \ if \ someone \ took \ a \ family \ of \ polar \ bears \ and \ dump \ them \ in \ Antarctica.\)
 
BigGlenn:

Yes I realized this after I posted the statement about it being a large sphere with a large cylinder cut out, or a small sphere with a small radius cylinder. I thought about it a bit more (tempted to google it the entire time) and decided that the question had to make sense, otherwise it would not be a riddle. So if the question made sense, it must not depend on the radius, which was when I came up with 36pi.

I haven't posted merely because others have already answered it in the in between time whilst I was thinking about it, and I figured it would be redundant to post the answer again.
 
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