[Guest]

In a far² parallel dimension... on a tiny pink planet, Zearth, evolve the first 2 intelligent bacterial beings, Fred and Frank. In fact they are so intelligent, they even know that they are the only life that exists. Each "intelligent bacterium" splits into two at the end of each day. Life in this universe can not die.

On day 1, Fred creates the universe's first telephone. Fred also appoints himself the universal telephone operator and assigns himself the number "0". He assigns Frank the number "1". On day 2, two new members are introduced to the universe, Fred assigns the new members telephone numbers "2" and "3".

On Day 3, there are 8 beings.... On day 4, there are 16 beings, and Fred realizes a PROBLEM, bacteria can't tell up from down! So #6 and #9 would keep getting each others calls. So he decides to avoid both.

Summary of the facts.

1) Day one > 2 bacterium, day two > 4, day three > 8, day four 16..... so on

2) Bacterium can't tell up from down (Fred avoids all flip-able numbers.. '6' and '9' are out, '161' and '191' are out)

3) Every bacterium gets a telephone number (1,2,3,4,...1243.....123456...)

Question: What is the sum of all the telephone numbers in the universe on the 100th day.

Bonus: If you are a bacterium spawned on the 101th day, what is the chance your telephone number will have at least one 6 in it.

[Guest]

To remove any confusion...

1869 and 6981 are not allowed.

However 1881 is allowed as it is the same any way you look at it.

[Glycereine]

No chance. 6 and 9 were eliminated

Edit:

I misunderstood. Thought no 6's or 9's would be used. You meant the number as a whole being flippable. I need more time now and to do the first part :-p.

Edited June 8, 2009 by Glycereine

[Guest]

I think I see a pattern after a few days, just not sure how to give an answer yet.

edit: removed spoiler for bonus, because Glycereine beat me to it.

edit:spelled Glycereine wrong....twice

Edited June 8, 2009 by James8421

[Glycereine]

I think I see a pattern after a few days, just not sure how to give an answer yet.

edit: removed spoiler for bonus, because Glycereine beat me to it.

edit:spelled Glycereine wrong....twice

Actually I spelled Glycerine wrong. But it was intentional .

I'm struggling with where to go on this one too after a couple days I have some reasonable ideas but not to go all the way to 100 yet...

[Guest]

I don't get it. if everyone has a unique number, then if there are 2^100 bacteria there are 2^100 numbers.

the 101st generation should start at 2^100 +1. However they will lose numbers: 6,9,16,19,61,69,91,96,106,109,161,191,601,609,611,901,906,911,619,916,10601,1090

1,11611,11911,etc.

I haven't found a definitive pattern yet

[Glycereine]

Keep in mind they also lose 18, 68, etc.

I don't get it. if everyone has a unique number, then if there are 2^100 bacteria there are 2^100 numbers.

I haven't found a definitive pattern yet

the 101st generation should start at 2^100 +1. However they will lose numbers: 6,9,16,19,61,69,91,96,106,109,161,191,601,609,611,901,906,911,619,916,10601,1090

1,11611,11911,etc.

[Guest]

thank god they eliminated number 666 i wouldn't want to have that one

oh i forgot that 8 is flippable thanks.

Edited June 8, 2009 by gkibarricade

[Guest]

there are 55 omited #s through the first 10 generations. so my guess is 550. lol

i don't think there is a solid stragedy

[Glycereine]

there are 55 omited #s through the first 10 generations. so my guess is 550. lol

i don't think there is a solid stragedy

Unfortunately I'm agreeing with you on this for the moment.

I started bruteforcing it and decided it wasn't worth it lol. Unless I can figure something else out I'll have to wait for a solution.

[Guest]

It's a simple math problem. If the 6 and the 9 are thrown away, 2 numbers are thrown away for every ten except for the 60's and the 90's which are all thrown away. That means that by day 100 with 2 numbers assigned a day, there would be 47 numbers thrown away. That means that the factorial of 147 would add to the total of everybody, including the ones that have been thrown away. To factor in the ones that have been thrown away, these must be subtracted from the factorial. The summation of these numbers and the net result is given. The 645 and 945 are the sums of the 60's and 90's respectively.

14 13

147!-E(10x+6)-E(10x+9)-645-945

x=0 x=0

The net sum of all numbers 0-147 that do not include a 6 or a 9 is

5852

[Guest]

you should avoid saying any of these problems are simple because invariably if you think its simple your wrong

just some advice plus if i skimmed your post right you forgot to omit 18 and similar numbers without 6 or 9 that are reversable any number with only 0's 1's 6's 8's and 9's (except as adiace said 1881 and numbers of similar synergy) are thrown out for example im pretty sure 26 doesnt flip over or 64 however 1698 and 1818 do

anyway thats how i understood it

[Glycereine]

It's a simple math problem. If the 6 and the 9 are thrown away, 2 numbers are thrown away for every ten except for the 60's and the 90's which are all thrown away. That means that by day 100 with 2 numbers assigned a day, there would be 47 numbers thrown away. That means that the factorial of 147 would add to the total of everybody, including the ones that have been thrown away. To factor in the ones that have been thrown away, these must be subtracted from the factorial. The summation of these numbers and the net result is given. The 645 and 945 are the sums of the 60's and 90's respectively.

14 13

147!-E(10x+6)-E(10x+9)-645-945

x=0 x=0

The net sum of all numbers 0-147 that do not include a 6 or a 9 is

5852

1. the only 2 days that have only 2 numbers assigned are day 1 and 2. Remember the polulation is doubling each day not increasing by 2 each day.

2. Remember you cannot use numbers that contain only 1's and 8's (unless completely symetrical) or that contain any 6's or 9's and only 1's or 8's or 0's as other numbers (ie 109, 18, 68, 1968, etc.) unless it cannot be flipped (ie it ends in 0)

Edited June 9, 2009 by Glycereine

[Guest]

Question: What is the sum of all the telephone numbers in the universe on the 100th day.

Bonus: If you are a bacterium spawned on the 101th day, what is the chance your telephone number will have at least one 6 in it.

2 on the power of a hundred is the number of telephone numbers

2 on the power of a hundred expressed in octal numerical base would be how the last bacteria's number would look like

the chance of of having a six in the number if you are spawned on the 101th day equals the chance of Fred losing his mind and ignoring his own rules on the 101 the day... 0%

EDIT: I said how the number would look like in octal form, since I didn't count 1 as flippable.

Edited June 9, 2009 by Randoms

[Glycereine]

2 on the power of a hundred is the number of telephone numbers

2 on the power of a hundred expressed in octal numerical base would be how the last bacteria's number would look like

the chance of of having a six in the number if you are spawned on the 101th day equals the chance of Fred losing his mind and ignoring his own rules on the 101 the day... 0%

EDIT: I said how the number would look like in octal form, since I didn't count 1 as flippable.

Unfortunately the number of phone numbers is pretty easy, but that's not what he's asking . He wants the sum of all the phone numbers, ie 0+1+2+3+4+5+7+8+10+11....

Also forgive my ignorance but what is octal numberical base?

I think you looked at the chance of a 6 the same way I did in my first post, but then I realized I was wrong. Just because it has a 6 or a 9 in it doesn't mean it's a flippable number.

[Guest]

Unfortunately the number of phone numbers is pretty easy, but that's not what he's asking . He wants the sum of all the phone numbers, ie 0+1+2+3+4+5+7+8+10+11....

Also forgive my ignorance but what is octal numberical base?

I think you looked at the chance of a 6 the same way I did in my first post, but then I realized I was wrong. Just because it has a 6 or a 9 in it doesn't mean it's a flippable number.

Ooh, English is not my native, I initially thought he wanted the number of telephone numbers. octal numeral base is what I wanted to write, but once agian, English is not my native.

It just sort of seemed to me, that both questions were in fact trick questions.

[Guest]

I'm sorry, I forgot that it was increasing exponentially not linearly. Brute force methods would take forever and the numbers are scattered throughout without any real pattern.

[Glycereine]

Ooh, English is not my native, I initially thought he wanted the number of telephone numbers. octal numeral base is what I wanted to write, but once agian, English is not my native.

It just sort of seemed to me, that both questions were in fact trick questions.

Sorry Randoms I wasn't criticizing your English, I don't know what octal numeral base is either, I was just curious. I'll look it up.

Cheers!

[Guest]

Sorry Randoms I wasn't criticizing your English, I don't know what octal numeral base is either, I was just curious. I'll look it up.

Cheers!

Looked it up for you octal numeral system : http://en.wikipedia.org/wiki/Octal

[Glycereine]

Looked it up for you octal numeral system : http://en.wikipedia.org/wiki/Octal

Thank you! Educational and interesting too

[Guest]

you should avoid saying any of these problems are simple because invariably if you think its simple your wrong

just some advice plus if i skimmed your post right you forgot to omit 18 and similar numbers without 6 or 9 that are reversable any number with only 0's 1's 6's 8's and 9's (except as adiace said 1881 and numbers of similar synergy) are thrown out for example im pretty sure 26 doesnt flip over or 64 however 1698 and 1818 do

anyway thats how i understood it

That is a start... if a number is made exclusively of the digits 0,1,6,8, and 9 then it will be removed (5^n such numbers, where n = number of digits). But this also includes 18181 and other symmetrical numbers.

[Guest]

1. the only 2 days that have only 2 numbers assigned are day 1 and 2. Remember the polulation is doubling each day not increasing by 2 each day.

2. Remember you cannot use numbers that contain only 1's and 8's (unless completely symetrical) or that contain any 6's or 9's and only 1's or 8's or 0's as other numbers (ie 109, 18, 68, 1968, etc.) unless it cannot be flipped (ie it ends in 0)

Fred thinks "10" is flip-able and will not use the number... He has no bias against "0"... infact... he is fine with assigning someone the number "043242", he will also assign the number "01010"

[Guest]

1. the only 2 days that have only 2 numbers assigned are day 1 and 2. Remember the polulation is doubling each day not increasing by 2 each day.

2. Remember you cannot use numbers that contain only 1's and 8's (unless completely symetrical) or that contain any 6's or 9's and only 1's or 8's or 0's as other numbers (ie 109, 18, 68, 1968, etc.) unless it cannot be flipped (ie it ends in 0)

Fred thinks "10" is flip-able and will not use the number... He has no bias against "0"... infact... he is fine with assigning someone the number "043242", he will also assign the number "01010"

[k-man]

Fred thinks "10" is flip-able and will not use the number... He has no bias against "0"... infact... he is fine with assigning someone the number "043242", he will also assign the number "01010"

Is 01010 the same number as 1010 and the same as 00001010?

[Guest]

Is 01010 the same number as 1010 and the same as 00001010?

no they are unique

[k-man]

no they are unique

Then I'm confused...

The OP says (or at least implies) that the numbers are assigned sequentially 1, 2, 3, ... How does Fred assign someone a number 01 or 001 or 000001?