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+--- Thread: 300 posts! (/thread-2358.html)
300 posts! - geodave - 21-Feb-2012
Well, I'm partial to squares (4, 9, etc.) because of the open locker problem*, among other reasons.
Also, DNA is base 4, so it's sort of built-in.
* Take 100 school lockers (numbered 1-100). Open every one. Close every second one. Toggle (open or close) every third one, etc. Which lockers are left open at the end?
300 posts! - BitBuster - 21-Feb-2012
Ah.
Any defenders for the poor base-3 system?
300 posts! - KeyboardWielder - 21-Feb-2012
Quote:Any defenders for the poor base-3 system?
Problem: Break a 40 kg weight into 4 pieces such that those pieces can then be used to measure any (integer) weight from 1 to 40 kg using a balance.
Solution uses balanced ternary (digits: -1, 0, +1).
- Madhav.
300 posts! - KeyboardWielder - 21-Feb-2012
Quote:* Take 100 school lockers (numbered 1-100). Open every one. Close every second one. Toggle (open or close) every third one, etc. Which lockers are left open at the end?What exactly do you mean by "etc."?
- Madhav.
300 posts! - Ida - 21-Feb-2012
Quote:What exactly do you mean by "etc."?
Hm, do you stop after 50? Or continue til 100?
Quote:Solution uses balanced ternary (digits: -1, 0, +1).
What exactly do you mean by that? (I have no clue.)
300 posts! - tensorpudding - 21-Feb-2012
Given he was talking about squares, I assume he goes up to 100. If the problem were to continue "for every number n from 3 to 100,, go through and toggle every locker that is a multiple of n", then the lockers open at the end would be lockers which are squares, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
300 posts! - James - 21-Feb-2012
Quote:What exactly do you mean by that? (I have no clue.)
Balanced ternary
(there's actually a level in my upcoming set with it as a theme...lol)It's base 3, but the digits are -1, 0, 1 instead of 0, 1, 2.
300 posts! - Flareon350 - 21-Feb-2012
I'm going to be completely honest here:
I have no idea what the heck base systems are
300 posts! - BitBuster - 21-Feb-2012
Quote:Hm, do you stop after 50? Or continue til 100?
If I remember the problem correctly, you keep going until 100.
Quote:I have no idea what the heck base systems are
You're not missing out on much.
300 posts! - tensorpudding - 21-Feb-2012
Quote:I have no idea what the heck base systems are
It's not hard. We use the decimal or base 10 system. In this system there are 10 digits, 0 through 9, representing each number less than 10. Each number N is represented by a list of digits, which are determined by finding d_1, d_2 etc. such that N = d_1 + 10*d_2 + 100*d_3 + 1000*d_4 + ... and so on until we reach a power of 10 larger than N. We write numbers using this series of digits in opposite order from how I wrote them there.
Ex: 1028 is 1*1000 + 0*100 + 2*10 + 8
In an alternative base system it's the same thing, only 10 is replaced by some other number, and there are a different number of digits, which may be represented by some smaller set of numbers or it might have 0-9 plus extra symbols if the base is larger than 10.
Ex: In base 2, one has the digits 0 and 1 representing the numbers less than 2. A number can be represented in binary with digits d_1, d_2 etc. such that N = d_1 + 2*d_2 + 4*d_3 + 8*d_4 + ... and so on until we reach a power of 2 greater than N. Remember that these d's are required to be 0 or 1, they are not allowed to be anything else.
234 in binary, for example, would be 1*128 + 1*64 + 1*32 + 0*16 + 1*8 + 0*4 + 1*2 + 0*1, so we would write it as 11101010.
The base 2 system is very popular because it is used by computers to represent numbers, because computers store and operate on data as a series of on/off states, which are made to represent numbers in binary.