The worlds first riddle!

[size=8]LARGEST KNOWN PRIME PALINDROME
150007 digits (as of Jan.)[/size]

In base ten, 11 is the only palindromic prime with an even number of digits. ~ You are a tricky dickie!


BTW did you notice a friend of yours paid a visit, is it your turn to carry out the medical?



Last night Shari and I were having a heated discussion over; What is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1

Can anyone assist?

Our heated "discussion" had nothing to do with that! As I recall, it was something about the amount of clothing articles that were accumulated on the the floor of your bachelor pad after our bout with a deck of cards.

I knew it had something to do with sum ?'Reciprocated' to one, when you raised two pair

Yes - it was a trick question.


Huh?


Do you mean:
What is the largest integer that cannot be written as a sum of distinct integers whose reciprocals sum to 1, or are all real numbers allowed?

"Huh?"

Butterfly called by!

"Do you mean:"

The former (it's a two digit number) with NO tricks

[size=8]RECIPROCALS SUM TO ONE
I would never have gotten this without the 2-digit hint. I modified a program that prints all partitions of a number to consider only partitions with distinct elements. I summed the reciprocals and checked for a total of one. Because of your hint, I started at 99 and worked backward.
The closest you can get with 77 is 1.0000009.

Do you know of a proof that 77 is the max?[/size]

Yes, I noticed. What's up with "bookmark?"

Mark:

LONG ROPE
You could probably lift it about 8 feet (depends on how tall you are).

It can be lifted 13.4257 feet.



From goal post to goal post is 120 yards = 360 feet.
From one goal post to the 50 yard line is 180 feet.
If one foot is added to the roap, then the total length is 361 feet.
When I lift the rope at the 50 yard line it forms two right triangles
The hypotenuse of each right triangle is 180.5 feet and the base is 180feet.
Use Pythagorean Theorem to solve for height.
(180.5)^2 = (180)^2 +h^2
32,580.25=32,400 +h^2
h^2 = 180.5
h = 13.4257 feet.


It's even more incredible when you figure that by adding only 1 inch, you can then lift it: 46.48 inches! At the fifty yard line.




What is the smallest number with multiplicative persistence of 11?
SUPER BOWL
277777788888899





What may I ask is the smallest number (besides 1) which is one less than twice it's reverse
REVERSE * 2 - 1
73



What is the largest ?'proven' palindromic prime


LARGEST KNOWN PRIME PALINDROME
150007 digits (as of Jan. )


Keep up to date dude;

February 2, 2006

Harvey Dubner retakes the palindromic prime record
10^150008 + 4798974 * 10^75001 + 1

Congratulations with this number of 150009 digits!




What is the largest integer that cannot be written as a sum of distinct integers whose reciprocals sum to 1


RECIPROCALS SUM TO ONE
I would never have gotten this without the 2-digit hint. I modified a program that prints all partitions of a number to consider only partitions with distinct elements. I summed the reciprocals and checked for a total of one. Because of your hint, I started at 99 and worked backward.

(You are a darn genius)


The closest you can get with 77 is 1.0000009.


Do you know of a proof that 77 is the max?


(Strangely enough, I cannot find one anywhere. Although 77 is accepted as the correct answer, it must have been proved by someone. I will enquire further)




(Butterfly called by!)

"Yes, I noticed. What's up with "bookmark?""


I was going to ask you the same question. Perhaps she was offering a gift, as in; Do you want a book Mark?







I know this is hard to believe, but: When I got back last night I found Butterfly and Shari sitting in the spa tub arguing over the number of three digit palindromic primes.

As you can imagine I did not want to take sides, and in any event, I thought them both wrong. Can anyone assist in the total number of palindromic primes consisting of three digits

Thank you.

[size=8]THREE-DIGIT PALINDROMIC PRIMES
101, 131, 151, 181, 191
313, 353, 373, 383
727, 757, 787, 797
919, 929

That makes 15.[/size]

Mark:


THREE-DIGIT PALINDROMIC PRIMES
101, 131, 151, 181, 191
313, 353, 373, 383
727, 757, 787, 797
919, 929

That makes 15.


Thank you for the total; it would appear at first glance that the ladies were right. I shall not glance again.



There I was, stripped to the waist down at the old forge, sweat running freely in the face of the searing heat, when Butterfly whispered, "The year 2002 is a palindrome." I barely had time to digest this little gem when, Shari leaned over and said, "So was the year 1991."

Ho-Hum you say? Well, through the white hot heat the sparks really flew as I hammered away until it occurred to me to ask:


a) When was the previous occurrence of two palindromic years in one person's average lifetime

b) When will the next be

c) What is the next normal palindromic year

Observant readers may remember crafty Mark's riddle:


?'smeteltoumies'

(The proper noun in my puzzle is much more commonly known (although it does include an abbreviation). The proper noun is the name of a city.)


This is driving me crazy, I can come up with;

OMIT ME(in)SALUTES

MA (in) SEMI OUTLETS


These are undoubtedly incorrect. Can anyone come up with the answer?

[size=8]PALINDROMIC YEARS
a) 999, 1001 (could also include some of 919, 929, 939, 949, 959, 969, 979, and 989)
b) 2992, 3003
c) 2112[/size]

smeteltoumies
It's a midwestern city.

Mark:


PALINDROMIC YEARS
a) 999, 1001 (could also include some of 919, 929, 939, 949, 959, 969, 979, and 989)
b) 2992, 3003
c) 2112


Thanks Mark, I owe you big time.






I had to laugh when Shari challenged me to a ?'truth or dare' match. I stopped laughing when she said, "I'll go first".


What is the smallest abundant number that is not the sum of some subset of its divisors



Note: An abundant number is a positive integer n for which:
S (n) = sigma (n) - n > n

(The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... Abundant numbers are sometimes known as; Excessive numbers.)

Fearing ridicule, I told her I had to return some overdue library books and I would answer upon my return. Please help, what is the friggin number. I may be onto a good thing here!

[size=7]St Louis[/size]



[size=7]The number 70[/size]

owlette: That's the city, but not the complete solution.

Li'l Owl, a.k.a. Owlette, may I thank you for your most timely intervention. You will undoubtedly be blamed for saving what's left of my sanity, and for that; I will be eternally grateful. By eternally, I mean; for a day or two.

"That's the city, but not the complete solution."

I must admit I would never have come up with the answer. However, once you take the city out of the equation could you not meet me halfway?

Great problem Mark.




SOALUCTIIDON

Could it possibly be:

[size=7]ACID (in) SOLUTION[/size]

Damn! I mean congratulations Li'l Owl, you are good.
However, this one should slow you down a bit.

Question:

1/6 of a sheep =



Due to circumstances beyond my control Butterfly is excluded form giving an answer. (Again)

Well I think you fleeced me this time!