OMG! The officers are total geeks!

[Selassie]

Hello,

Over quite some time, the officer forum has been spammed up with these silly erhm.... math riddles.

I am going to post some of them here, just because maybe some of you will solve them. Or maybe you will simply start trusting us more when it comes to certain tactical aspects or roster balance.

But mostly, it is a call for sympathy. Sympathy to our poor Verv. Look what she has to stand for! You should give her a round of applauds for her patience.

[Selassie]

First of, The magic number challenge!

First to solve/answer something correct=Sini

Based on today`s TS chat:



One can say 142857 is a fun number in this aspect. If you multiply it by 1, 2, 3, ..., NoOfDigits, the results are all the cyclic permutations (i.e. the same digits in the same order with a different starting digit).

It is currently known that 142857 is the only number with such a property if you don`t allow zeros to be digits. If you allow zeros to be digits, then there are other such examples. What does it mean to allow zeros? Well, to consider a number like 03456 (thus, adding a 0 as the first digit, which basically does nothing).


(and so on)

Of course, this number doesn`t satisfy the "being nice" condition (i.e. the digits of it`s multiples are cyclic permutations), but it explains what the "allowing zeros" part is.

Math challenge: Find another number like 142857!

Can you solve/answer?

[Selassie]

BTW (so you understand Flipp's comment), the title of the original thread was "Therapy"

the title of this topic should be a strong hint to both of you....

The challenge of Flipp's name!
Best solution by Row

Math challenge: Adding together the numbers you get swapping each letter from "FLIPPANTINE" with it's ascii decimal value, you get 70+73+80+80+65+78+84+73+78+69=670

Get 670 to 1337 using as few operators as possible.
 - You may not use + or -
   (meaning 670+667 won't qualify as getting there in 1 operator)
 - You may only operate with 1 digits, no decimals (meaning only 0-9)
  (meaning [tex]\frac{670\cdot19955223880597014925373134328358}{10000000000000000000000000000000}{[/tex] won't qualify as getting there with 2 operators)
 - Any decimals produced is to be truncated at each operation.

How few operators do you need?

How many operators do you need?

[Monascha]

First of, The magic number challenge!

First to solve/answer something correct=Sini

Can you solve/answer?

0588235294117647

now something i really need to use my brain for pls 

[Selassie]

A classic with a added twist
Solution by Row

By popular demand!

There was a mighty emperor, in times long-forgotten. He loved wine, and such, the people decided to present him a gift of 1000 wine bottles. However, he had hidden enemies, and one (exactly one) of the bottles was poisoned. In order to determine which one it is, the high council ordered some prisoners to "taste" each bottle.
There was a problem though, the poison effects were only visible after 15 days (exactly 15), so if one prisoner would taste the poisoned bottle on the 3rd, he`d die on the 18th; if he`d taste it on the 7th, he`d die on the 22nd and so on.
There was a deadline, too. For simplicity, let`s say it was the 1st of April! The deadline was the 24th of April. At the end of that day, they needed to give the bottles to the emperor, and they couldn`t risk to have him killed!
Here`s the question: what is the minimum number of prisoners required in order to have guaranteed success?

Example: With 1000 prisoners, they can test one bottle each. This way they`ll find out in time which the poisoned bottle is. However, it can be done with less prisoners, the question is what`s the minimum

@Row: find the general formula! (N bottles, poison effects visible after exactly P days, deadline is D days, [tex]D \geq P[/tex])

Now, the classic version has a the same deadline as the time it takes for the poison to kill.

Can you solve the classic version? (Normal mode)
Can you solve Maky's version? (Heroic mode)

[maky]

0588235294117647

now something i really need to use my brain for pls 

General formula (+proof )

[Monascha]

A classic with a added twist
Solution by Row

Now, the classic version has a the same deadline as the time it takes for the poison to kill.

Can you solve the classic version? (Normal mode)
Can you solve Maky's version? (Heroic mode)

First day they can check for poison is april 16th (15 days after april 1st). So in total, they have 9 days to check for poison (april 16th to april 24th). 1000/9 = 111,11111111

So they need 112 prisoners to be sure to find the poison on the deadline date.

and sorry, i suck at latex xD

[maky]

Can be done with less

[Monascha]

General formula (+proof )

1/7 = 0.142857 => 142857

1/17 = 0.0588235294117647

1 x 0588235294117647 = 0588235294117647
2 x 0588235294117647 = 1176470588235290
3 x 0588235294117647 = 1764705882352940
4 x 0588235294117647 = 2352941176470590
5 x 0588235294117647 = 2941176470588230
6 x 0588235294117647 = 3529411764705880
7 x 0588235294117647 = 4117647058823530

I forgot the exact explanation (something about 7 and 17 prime numbers), but my former math teacher was always showing us stuff like this...somehow the it stuck  

next number where this works is 19 or 23 i believe
 

[Monascha]

Can be done with less

yeah, i kinda expected that this was too easy. Will have a look at it tomorrow 

[Monascha]

Can be done with less

Ah, you do not need 112 prisoners, but 112 bottles (or 111,11111) need to be tested every day. You need to number those bottles and assign a certain number of prisoners to drink from certain bottles. And by elimination you can determine which bottle is poisoned.

with 1 prisoner, you can test 2 bottles and this number doubles with every prisoner you add. So with 7 prisoners, you can test 128 bottles a day (2=4, 3=8, 4=16, 5=32, 6=64).

[maky]

Ooh that`s a really nice answer, and beats most of the "first-sight" solutions I`ve got (I gave this problem to our romanian national team, they had big difficulties with it ).
Even 7 can be improved though

[Monascha]

Ooh that`s a really nice answer, and beats most of the "first-sight" solutions I`ve got (I gave this problem to our romanian national team, they had big difficulties with it ).
Even 7 can be improved though

hmm, i think im overlooking something with the delayed effect of the poison but i've read the problem a few times now and really can't think of anything else atm 

[Kaasrasp]

MY EYES!



Oke, here's one. you probably all know it etc, but yea

Solve!
XXII
----      =   III
VII    

(Cant break the V or the X'es, and can only move 1 I)

[Monascha]

I do not have a calculation, but i think i know how to do it with less people.

If you want to do it with 6 prisoners, you can only sample 64 bottles and guarantee that the outcome is correct. So in order to sample more with 6 people, you need to run more experiments per day with different assignments. Since you know the time it takes for the poison to work and have 9 days available for testing, you should be able to determine what bottle was posioned by the number of deaths and their date.

Only downside in this scenario, is that all the prisoners will almost certainly die (where in my previous solution, 6 could be lucky)