Cryptograph - Cryptogram with a Picture

the daily puzzle over at this site
... there are some clues if you follow the link ...
... e.g. the first two words are the person's name ...

Just Plain Riddles

Found these short ones on a website:

1) What is it that you can break just by calling its name?

2) He who knows it, doesn't tell it. He who takes it, doesn't know it. He who has it, doesn't want it. What is it?

3) What must you keep, after giving it to someone else?

4) What belongs to you, but others use it more than you do?

Physics in All Directions

Question #1:
You are driving to a birthday party with a friend. You have a helium balloon suspended between you two in the front seat, not quite touching the ceiling. The road takes a sharp turn to the left, causing you and your friend to feel you are being pushed toward the right. Does the balloon lean toward you, or toward your friend?

Question #2:
You have a toilet, whose water jets are directed straight down the sides of the bowl, so that when you flush, the jets do not impart any rotation to the water going down. When you look down at the water flushing, in which direction does the water spin when you are in Ohio? In Austrailia? If you were at the North Pole?

Question #3:
A 33 foot tall hallow pipe is capped on one end, turned upright, and filled completely with water. Two sensitive pressure guages indicate the pressure near each end. You note that the bottom pressure is almost 15 psi higher than at the top. I take you and the device up in a helicopter, and drop everything from 5000 ft altitude. While falling, you ponder if there has been any change in the pressure gauges. What do you think in this situation?
Bonus: For how many seconds do you think you can remain focused on this problem, starting from when I drop you?
Extra bonus for showing back up at the helipad after I've done my part!

Hashiwokakero

or simple Hashi is another one of those wonderfuly addictive logic/math puzzles with a non-English name.

The Rules (from wikipedia):

Hashiwokakero is played on a rectangular grid with no standard size, although the grid itself is not usually drawn. Some cells start out with (usually encircled) numbers from 1 to 8 inclusive; these are the islands. The rest of the cells are empty. [Other sites report that there should be one and only one solution, a'la Sudoku]

The goal is to connect all of the islands into a single connected group by drawing a series of bridges between the islands. The bridges must follow certain criteria:

• They must begin and end at distinct islands, travelling a straight line in between;
• They must not cross any other bridges or islands;
• They may only run orthogonally;
• At most two bridges connect a pair of islands; and [so 0, 1, or 2 bridges may connect two islands, but no other number]
  
• The number of bridges connected to each island must match the number on that island

[NOTE: I will post the site I got the puzzle later ... it has a nice interface that makes trying solutions a lot easier, but I didn't want to give it away before someone figures it out the old way. :-p I am a mean bugger aren't I?]

ForC: Tar Filled Barrels of Resolute Avocados

ForC

1. In Scotland, the new year is ushered in by rolling flaming tar-filled barrels down streets (Jan-1)
   
2. Studies show that 12.5% of people drop their New Year's resolutions by week three (Jan-2)
   
3. Avocados have 60% more potassium than bananas (Jan-3)
   

** I got a Fact or Crap tear-away-a-day calendar as a Christmas gift and have brought it to work. I will try and post a few of the better ones once a week or so. I am keeping track of how many I get right/wrong by tacking them up in two stacks on my cube wall. If anyone wants to play along, you can leave your votes in the comments and I can post the answers the next time I add more (maybe even with some fancy graph to see who is leading.

If you want to look up the answers on the web, I am sure they are out there but please refrain from posting the real "answers" for at least a few days so that everyone has a chance to think about it. **

Scalable Solution

A Scalable Solution Might Be Key

Imagine a series of positive real numbers defined so that each next number is a direct math function of the one preceding it such that
every X_n = f(X_n-1)

Require further that after the function is applied about 5 to 25 times the number ends up exactly doubled, that is every X_n = 1/2 X_n+j where 5 <= j <= 25

In other words, I want all series members to always have the same relationship to their adjacent members AND I want the series to require about j steps to achieve a doubling.

---------------------------------------------------------------
Puzzle #1:

Can you find a function that would accomplish this for any given j in the range?

---------------------------------------------------------------
Puzzle #2:

Consider the j members that fall between any pair of members in a 2:1 ratio.

Can you select an ingenious value of j such that some of the in-between members are also in nice small integer ratios to the starting member, e.g. in a 3:2, 4:3, or 5:4 ratio?

i.e. where the series looks something like
X₁, . . X_a~1.25X₁, . . X_b~1.33 X₁, . . X_c~1.5 X₁, . . X_j=2 X₁

---------------------------------------------------------------
Puzzle # 3:

How is it that almost everyone has listened to this hundreds of times before but few have ever heard it put this way?

Dang Words

How many words can you find in the english language that begin with the letters dw- ? Multiple forms of the same word and compound phrases using the same word do not count (e.g. if the word is paint, you cannot also cite paints, painted, painting; if the word is book, you can't also cite books, book shelf, etc.). Also poorly pronounced words don't count (e.g. "Gimme 'nother D'wers on the rocks").

Some can be found here.