Alternative Recursion

palindrome Pangram Puzzle – a work in progress

Definitions:

A palindrome is a sequence of words like "lid off a daffodil" or "shallot ayatollahs" that uses the same letters reading backwards as forwards.

A pangram is a sequence of words that contains every letter of the alphabet (at least once).

Puzzle:

Find the shortest sequence of words that is both a pangram and a palindrome.

The sequence need not form a meaningful or grammatical sentence.

Use this dictionary: WORD.LST

from ITA Software

is this solvable with 1 man’s resources and timeframe?

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#word problem, but first: why I’m an idiot:

So I’ve been working on this little puzzle:

“If the integers from 1 to 999,999,999 are written as words, sorted alphabetically, and concatenated, what is the 51 billionth letter?” from ita software

I outlined the framework of an algorithmic solution months ago when I first saw it, and i solved it with maple, but never got to implement it using a ‘proper’ programming language.

This problem came to mind again recently as a fun excuse to get my hands dirty with a computer programming language called python.

I’ll start at the end, and say I was totally frustrated, because my seemingly perfect algorithm gave the wrong answer, in spite of passing all sorts of verification tests… I finally got to the point I was so convinced that unless I failed to spell the 27 numbers in my native language’s naming scheme, the problem’s hint must have been wrong…. >>>

so 40 is ‘forty’, not ‘fourty’.  and then everything worked perfectly…

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for anyone who does sudoku on the metro:

If you picked up a newspaper with sudoku which was all wet and smudged,

and all you could read was this:

Can you fill in any other blocks to match the solution of the described sudoku puzzle?

if so, which ones, with what numbers, and why?

<note: comments might contain spoilers>

puzzle.2b

draw 7 points on a plane

such that exactly 3 lines can be drawn which contain only 2 points.

Puzzle.2a

for all n larger than 5:

how can you arrange n points (not all in the same plane),

such that the plane of any 3 points contains at least four?

Puzzle.1b

Exactly how big is the smallest circle which can contain 3 non-overlapping coins with radii ‘r’ ?

solutions and/or hints may appear in the comments.

puzzle.1a

Exactly how big is the smallest (in area) triangle which can contain 3 non-overlapping coins with radii of ‘r’?

solutions and/or hints may appear in the comments.