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.

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?"

[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

[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.

[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!