Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 138
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The penultimate line:
Since the numbers n enumerate the whole range from 0 to 99, their sum modulo 100(S0) also falls into this range....
If n is numbers (1-100), then their sum modulo 100 is fixed.
If by n they mean f(n), then there is no way they can enumerate the whole range from 0 to 99, as there can be repetitions.
Right?
The penultimate line:
Since the numbers n enumerate the whole range from 0 to 99, their sum modulo 100(S0) also falls into this range....
If n is numbers (1-100), then their sum modulo 100 is fixed.
If by n they mean f(n), then there is no way they can enumerate the whole range from 0 to 99, as there can be repetitions.
Right?
No.
n is the internal number of each megamosk that the megamosk knows, from 0 to 99. They could have agreed.
f(n) is the actual number (the number on the cap) minus 1.
calc(n) is what the megamosk calculates and writes on the paper.
S(n) is the sum of all numbers seen by the megamoscope with internal number n. Of course, modulo 100. Each number is reduced by 1.
There is another cap problem coming soon.
If n is MM's assigned number for itself, then the sum of them modulo 100 will not be S0. Because S0 is the sum of all the numbers on the caps f(n).
And I'm not saying that, read it carefully.
S_0 is the sum of all the real numbers on the caps modulo 100. Each one is reduced by 1.
Real experiment: there are 5 MMs in total, they are written with numbers from 1 to 5 (not necessarily different). Let's say 2, 4, 4, 4, 2.
The megamoskies in their calculations make these numbers as follows: 1,3,3,3,1.
S_0 = 1+3+3+3+1 = 11 mod 5 = 1. This number is unknown to anyone.
MM #0 (on cap 2) writes (0 - 10) mod 5 + 1 = 0 + 1 = 1.
MM #1 (on cap 4) writes (1 - 8) mod 5 + 1 = 3 + 1 = 4.
MM #2 (on cap 4) writes (2 - 8) mod 5 + 1 = 4 + 1 = 5.
MM #3 (on cap 4) writes (3 - 8) mod 5 + 1 = 1.
MM #4 (on cap 2) writes (4 - 10) mod 5 + 1 = 5.
As we see, the second MM (with number 1) has a direct hit.
And I don't say so, read it carefully.
S_0 is sum of all real numbers on caps modulo 100. Each one reduced by 1.
Yes! But in the penultimate line of the answer: ...the numbers n enumerate the whole range from 0 to 99, and their sum modulo 100(S0)...
n is the contract number of the MM, S0 is the sum of the numbers on the caps. Different things. Apparently this is what Contender meant.
Yes! But in the penultimate line of the answer: ...the numbers n list the whole range from 0 to 99, and their sum modulo 100(S0)...
n is the contract number of the MM, S0 is the sum of the numbers on the caps. Different things. Apparently that's what Contender meant.
Yes, I got it. But what S_0 is, has been clearly defined before. I.e. you can just drop the strikethrough phrase from the proof:
...the numbers n enumerate the whole range from 0 to 99, andtheir sum modulo 100(S0)...
and rewrite the formula
calc(n) = (n - S_n) mod 100 + 1.
Now it's all clear. Good job!
I will be silent because I have solved most of the problems on the site and you are unlikely to ask the one that I have not scored =)
The only thing I will say right or wrong sometimes, so that people do not waste time waiting for your comments
Then solve a real problem: name areal household electrical appliance that has an efficiency factor of 100% to 5 decimal places...
ZS - braingames is good for learning. As far as I understand you all have already graduated from school - maybe it's time to tackle real-world problems?
ZS - braingames is good for learning. As far as I understand you all have already graduated from school - maybe it's time to solve real-world problems?
You're in the wrong place, sorry. The thread is called "Pure Maths...." and will remain so.
Here, in this branch, "realists" don't survive long(because, hiding behind "real" problems, they are usually very weak in problems, typical for this branch). And I advise you to change your tone of treatment from dismissive to respectful.
The problem you asked is, by the way, quite good. I don't know the answer yet. It was poorly presented.
P.S. Iron. All heat is useful, and almost all of it dissipates through the metal flat part, which is the functional part.
The second option is an electric kettle (with plastic walls).