Safecracker!

[KomradRikardo]

Difficulty: **

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A seasoned thief is trying to break into a safe. He finds a dial with positions numbered 00 to 99, and the following message:

ABOUT THE COMBINATION:
I consist of three two-digit segments, i.e. the form XX XX XX.
All three numbers are divisible by 3.
The middle, and only the middle number is odd.
The third number is not divisible by the first number.
The first number is divisible by the middle number.
The sum of all three numbers is the reverse of the first number.
The third number with digits reversed is double the middle number.

What is the combination to open the safe?
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_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[yuethomas]

Answer: (18, 03, 60)
_________________
Tom Yue

[KomradRikardo]

THE STAGE MANAGER

Difficulty: ****

The stage manager opened the back door to the theatre and went in to prepare the stage. Tonight was going to be a special act. But just as he went to raise the slatted cover and access blind behind the stage, he noticed it was protected by two combination locks of some kind. They respectively used combinations of the form XXXXX and XXX. The numbers had of course been scrambled, but beside the locks lay the following peculiar note:

I am prime.
Remove my first digit and I remain prime.
All my digits are prime, save one.
The sum of my first digit and my last digit equals my second digit.
The sum of my second digit and any other digit save the fourth, is prime.
My second digit is not divisible by my last digit.

I am divisible by the sum of the digits of the other number.
The sum of my first digit and my second digit equals my last digit.
Add one and I become prime.
I cannot be made prime by removing just a single digit.
I may prove ambiguous, but in any case I will ultimately make sense using only one value.

With the right combination the performance tonight will be congenitally productive.

Who was going to perform on stage that night?

NB a bit of brief research may prove necessary, but it should be no more than superficial front page googling.
_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[Laramie]

Well, the first one is 58573 and the second one is one of 112, 336, and 448.

[Highest Prime]

Did somebody call?

I've gotten that the combinations are 58573 and either 336 or 448 ...

... but unless the special performer is the Strasburg, ND high-school marching band, I'm stumped - and Google is proving no help.

H'

[KomradRikardo]

Excellent solving!

However, the second stage has to be solved. Note the last line of the message. There are no zip codes involved in this...
_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[Highest Prime]

Googling "congenitally productive" produces a grand total of 0 hits. (Wow ... I didn't think there was such a thing in Google any more! Does this mean that when this GL page next gets crawled, that phrase will become a Googlewhack? To potentially be involved in the making of Internet history ... ah, the excitement!)

Trying various forms of the unique words in the last line with the determined combinations likewise yields nothing meaningful. Perhaps another clue is in order?

H'

[Laramie]

Observation: We can turn the numbers upside down to get ELSBS and either BHH or GEE. Those don't seem to anagram to anything useful (unless you count "L' Bee Gees" ).

[KomradRikardo]

But sire, that is the clue! Think about it and its meaning carefully. (There is a slight play on words - Ed.) Now you have the combinations, what might one do next? The fact that one of the numbers is prime does carry some significance in the first place...

(and I'm sure (s)he'd be chuffed at being confused with a marching band from a high school in North Dakota... )
_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[dave10000]

[Laramie]

Bumpity-bump

[KomradRikardo]

Cheers, Laramie. BTW I can't really help out a lot more on this one because any further hints beyond those already given would essentially be a spoiler. (Obs: IMHO - Ed.)
_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[KomradRikardo]

This has nothing whatsoever to do with the above.
_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[baraka]

Well, I am thinking that Kylie Minogue will be performing.

Arrived at by multiplying the two combinations together, 58573 and 336, ("productive") and getting 19680528. And Kylie Minogue was born on May 28, 1968. ("congenitally productive")

[KomradRikardo]

THE STAGE MANAGER'S EMI VISIT

Difficulty: ***

Since the last performance went off spectacularly (after figuring out how to unlock the stage!), the stage manager received a special invite to EMI headquarters. What a privilege, he thought, and needless to say, arrived for his privileged appointment in very good time. However, instead of the explosively warm welcome anticipated, those practical jokers had evidently been at work again and our hapless fellow was greeted with the following sign at the door:

Welcome to EMI. Privileged access to this area is granted only to those who know all ten "magic" numbers. We have a shortcut for remembering them, but you cannot realistically be expected to know that off by heart. In that case, you will just have to find them out by your own means. All numbers contain four digits or fewer and use the common decimal system, no other base.

All ten numbers are even.

The first number is 1000.

The second number is 8400.

The third number is the same as the last number and divisible by the first number.

The fourth number is the sum of the third number and half of the first number.

The fifth number contains no prime digits and no repeated digits, is divisible by both nine and ten but not twelve, and can be made prime by either adding or subtracting one.

The sixth number is equal to the ninth number minus the first number, or one and a half times the third number. When added to the fourth number and then divided by the first number, it becomes prime.

The seventh number contains three prime digits and at least two even digits, cannot be made prime by adding or subtracting one, but when divided by two becomes a prime containing only one prime digit. Its last digit is present only in two of the other numbers.

The eighth number contains only one prime digit and can be made prime by either adding or subtracting one. The sum of its digits is divisible by each of its first three digits. The sum of its two halves in the form of a pair of two-digit numbers added together is divisible by the second half of the seventh number. Its first digit is present only in two of the other numbers.

The ninth number contains only one prime digit and the sum of its digits is prime. The product of its first two digits is equal to the number comprised of its first three digits minus the fifth number. Its first digit is shared with, and present only in, two of the other numbers.

Time to help our man out with eight missing numbers!

BONUS: (Difficulty: *****) Could there really be any kind of "shortcut" or remotely logical link within this arcane bunch of numbers or is that just a bluff? (HINT: There is a direct connection with the solution to the previous Stage Manager conundrum that baraka correctly posted on 2006-11-12. Consider that there are ten numbers, logically valid at the present time, and think of the numbers in parenthesis in crossword clues. If this is worth attempting, that is all the information you need.)
_________________
--
KomradRikardo aka E.R.
May your puzzles be challenging and your solutions be rewarding!

[jesternl]

the 5th number is 90 I think.

But then I run into the following.
spoiler
the 1st number is 1000, and the 3rd and 9th number are divisible by 1000, so x000 (clue 3). Then take clue 9: "The product of its first two digits is equal to the number comprised of its first three digits minus the fifth number". This product is 0 since the 2nd digit of the 9th number is 0.
so x times 0 = x00 (since we don't yet know the first digit of the number) - 90. impossible.
the 5th number cannot end in 00, since there are no repeated digits in the it, so even if it is not 90, it'll never work.

Were do I go wrong?

[referee]

There are ten numbers.
_________________
Jan 21st, 2008: The pillaging continues.
Mar 4th, 2008: Rest in Peace, Gary Gygax. May your dice always roll a natural 20 wherever you are.

Be the Ultimate Ninja! Play Billy Vs. SNAKEMAN today!

[ralphmerridew]

The numbers are:
1: 1000
2: 8400
3: 5000
4: 5500
5: 810
6: 7500
7: 2234
8: 4260
9: 8500
10:5000

Either the line "9: The product of its first two digits is equal to the number comprised of its first three digits minus the fifth number." or the entire fifth clue is redundant.

[jesternl]