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.
Question
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.
Link to comment
Share on other sites
Top Posters For This Question
25
4
Popular Days
Jun 9
32
Jun 10
21
Jun 11
20
Jun 14
3
Top Posters For This Question
Glycereine 25 posts
k-man 4 posts
Popular Days
Jun 9 2009
32 posts
Jun 10 2009
21 posts
Jun 11 2009
20 posts
Jun 14 2009
3 posts
Posted Images
77 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.