[Quiz] Answer the Bitcoin question and earn merits! #4

[BlackHatCoiner]

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It's been a while since I published a quiz. It's time for another one. 

- What's this?

Bitcoin quizzes are technical questions of educational character that improve the average user's knowledge on Bitcoin, and help him rank up. You can read more about it in here.

Answer the questions that follow and you will earn merits. We have talked a lot about probabilities, such as the probability of reversing a confirmed transaction, or probability of finding a block within the next few minutes, but it's time for another kind of puzzle.


Let's suppose that the network's difficulty is 42 trillion, about half of what's today.

• The average block time of the current epoch (A) is 10 minutes, and we're close to the difficulty adjustment. Once we reach it, difficulty remains the same and we enter the next epoch.
• The average block time of the next epoch (B) is 8 minutes, and another difficulty adjustment occurs, which increases the difficulty, so that the average block time returns back to 10 minutes.
• The average block time of the next epoch (C) is 1 hour, due to a catastrophic decision made by the US government to seize all the miners.

What's the difficulty once it adjusts after epoch C?

[Aanuoluwatofunmi]

This can only be discovered by the available statistical numbers of miners at a particular given time competing for the block rewards, since it's approximately 10 minutes or less for a new block to be mined or rewarded, if the mining difficulty increases then the hash rate reduces and same applies if the hash rate increases the mining difficulty reduces.

The network calculates the total time it takes to mine the last 2,016 blocks. The ratio of the standard 20,160 minutes (10 minutes x 2,016 blocks) to the time it took to scale the last difficulty epoch is then multiplied by the most recent difficulty level. The calculation yields a result that will determine the required percentage change in the mining difficulty that will bring the block time to the desired 10 minutes.https://www.coindesk.com/learn/bitcoin-mining-difficulty-everything-you-need-to-know/

Mathematically

60 mins make one hour
10 mins average block time

60-10=50

50/10 =5

My answer is 5 minutes for average time and

5x20160x10=1008000 difficulty adjustment

[Edited]

[Hazink]

Using the available information above, I and my kid sister were able to come up with this:.



In short of the whole thing written down on the paper above:

Explaination:
Epoch will be represented by "Ep"
Difficulty by "Diff"
New by "N"

Ep A: Diff  = 42 trillion
Ep B: Diff increases by 25% (10/8) = 1.25
N Diff = 42 trillion × 1.25 = 52.5 trillion
Ep C: Diff decreased by 6 X (1hour vs 10 minutes)
N Diff = 52.5 trillion ÷ 6
Therefore the Diff after Ep C is = 8.75 trillion

[Bitcoin Smith]

Let's suppose that the network's difficulty is 42 trillion, about half of what's today.

• The average block time of the current epoch (A) is 10 minutes, and we're close to the difficulty adjustment. Once we reach it, difficulty remains the same and we enter the next epoch.
• The average block time of the next epoch (B) is 8 minutes, and another difficulty adjustment occurs, which increases the difficulty, so that the average block time returns back to 10 minutes.
• The average block time of the next epoch (C) is 1 hour, due to a catastrophic decision made by the US government to seize all the miners.

What's the difficulty once it adjusts after epoch C?

I am not that good yet with the technical terms but let's try my best and see whether it's right.

Current Network difficulty = 42 Trillion

Average block time of epoch c (target) = 1 hour

Average block time of epoch b (current) = 10 minutes

Now formula to find Difficulty Level = Difficulty Target/Current Target.

epoch c = 42 tril * (10/60 mins)

epoch c = 42 trillion *(0.16666666667)

epoch c = 7 trillion billion

Also, I read that there is upper limit and lower limit for the difficulty adjustment which can be either 300%+ or -75%

That means it can only goes down to 10.5 trillion

Bitcoin Mining Difficulty: Everything You Need to Know

the mining difficulty cannot be altered above or below four times the current difficulty level. The upper limit for each difficulty epoch is a +300% change, while the lower is a -75% alteration. This rule is put in place to eliminate any abrupt changes in mining difficulty.

[Amphenomenon]

Here is a quick Python script though is not really professional

Code:

#Difficulty when Average Time = 1 hour

ActualDifficulty = 2016 * 60 #Since the Average difficulty is 1hr = 60mins

ExpectedDifficulty = 2016 * 10 #Since the expexted average difficulty is 10mins

Difficulty = ExpectedDifficulty / ActualDifficulty

NewDifficulty = Difficulty * 42000000000000 #42 trillion which is the suppose difficulty before This NewDifficulty

print (NewDifficulty)

[Tungbulu]

[← Previous Question]

It's been a while since I published a quiz. It's time for another one. 

- What's this?

Bitcoin quizzes are technical questions of educational character that improve the average user's knowledge on Bitcoin, and help him rank up. You can read more about it in here.

Answer the questions that follow and you will earn merits. We have talked a lot about probabilities, such as the probability of reversing a confirmed transaction, or probability of finding a block within the next few minutes, but it's time for another kind of puzzle.


Let's suppose that the network's difficulty is 42 trillion, about half of what's today.

• The average block time of the current epoch (A) is 10 minutes, and we're close to the difficulty adjustment. Once we reach it, difficulty remains the same and we enter the next epoch.
• The average block time of the next epoch (B) is 8 minutes, and another difficulty adjustment occurs, which increases the difficulty, so that the average block time returns back to 10 minutes.
• The average block time of the next epoch (C) is 1 hour, due to a catastrophic decision made by the US government to seize all the miners.

What's the difficulty once it adjusts after epoch C?

In order to arrive at the difficulty after epoch (C) we should first consider the relationship between each epoch difficulty and the average block time, from the hypothetical scenario, we already know that the lesser the block time, the more the difficulty reduces and vice versa.

So if the average block time of epoch (A) is 10 minutes and the difficulty is around 42 trillion, and epoch (B)'s average block time is 8 minutes, the difficulty increases in order to maintain 10 minute average block time.
So if the average block time of epoch (C) should increase to 1 hour due to uncontrollable factors, like the US government deciding on seizing all the miners, the difficulty should drastically decrease significantly in order to be able to maintain 10 minutes average block time.

I stand to be corrected, but I think that if this is the case and epoch (C) is over 6 times higher than the target average time which is 10 minutes, the difficulty should be reduced by a factor of 6.

Since the initial difficulty (42 trillion) would be reduced by the factor of 6, the difficulty after epoch (C) should be decreased to around 7 trillion.

[Mia Chloe]

[Edit]
Initially radioed wrongly I'll be settling with this


My solving is very simple .
The Bitcoin network tries to balance the networks mining difficulty by increasing or reducing it depending on how fast the previous block was solved. Now the network protocol tries to make sure that the average time for solving a block doesn't exceed 10 mins but rather is within 10 mins.
Therefore to calculate the mining difficulty of the present Epoch C we have to first find the mining difficulty of Epoch A and Epoch B keeping in mind that the ratio for Epoch A is the standard value (20160 for 10 minutes).

After solving for Epoch B difficulty I then used it to find that of Epoch C by rationing their average time of Epoch B and Epoch C and multiplying with the difficult of B.

[EL MOHA]

Using the formula from https://learnmeabitcoin.com/beginners/guide/difficulty/

1. The difficult at 42 trillion and then the average time gets to 8 minutes for that reason we have the second difficulty to be

Expected/actual
Expected=2016x10=20160
Actual=2016x8=16128
20160/16128=1.25

Difficulty at 42 trillion x 1.25 = 52.5 trillion.

2. Then with the new difficulty at 52.5 trillion we then go to C where the average time is 1 hour (60minutes)
Expected/actual

Actual is 2016x60=120960
20160/120960=0.1667

With the difficulty at 52.5 Trillion
Difficulty x 0.1667= new difficulty
52.5 trillion x 0.1667= 8.75 Trillion as the new difficulty.

The percentage change though is
Change/original
Change = 8.75-52.5=-43.75
-43.75/52.5=-0.833x100

Change percentage is -83.3%

This is less than the bench mark of -75%

[hosseinimr93]

The answer is 13.125 trillion.

We have three difficulty adjustments.
As mentioned in the question, the difficulty remains the same after the first adjustment. So it would still be 42 trillion.
The difficulty after the second adjustment would be 42*10/8 = 52.5 trillion.
The difficulty after the third adjustment would be 52.5/4= 13.125 trillion. That's because the difficulty can't be decreased by more than 75%.

[Churchillvv]

Solution

2016 x 10 = 20,160

2016 x 60 120,960

Therefore;
20,160 ÷120,960
= 0.166

Given the old difficulty which is 42,
Hence;
= 42 x 0.166

= 6.972

Since number is less than 1 (blocks were mined slower than expected) the difficulty decreases when it reaches Epoch (c) to 6.972 trillion, but if the Epoch (B) has an effect on it it would result to and increase to a 8.715 trillion difficulty but if it doesn't then it remains at the initial result.

Every miner after US government release them   now works with this new difficulty for the next 2,016 blocks which is 6.972 trillion

[BlackHatCoiner]

For once more, hosseinimr93 is the first to actually answer with the solution. 

The correct answer is 13.125 trillion, because in the epoch B it increases by 25% (42 -> 52.5) and then decreases by 75% (52.5 -> 13.125). The trick of this quiz was the knowledge of difficulty adjustment restriction to a factor of 4, as shown in here: https://github.com/bitcoin/bitcoin/blob/4a020ca443ba370bf41583962d16aa8551876f53/src/pow.cpp#L54-L59. The reason we do not allow difficulty to grow beyond 300% or drop by less than 75%, is to achieve a middle ground between resilience in network disruption and quick response to a genuine change in the hashrate.

For example, in the extreme scenario that the US government shuts down large mining farms, and reduces the total hashrate by 83.3%, these miners can migrate their infrastructure elsewhere within the next month. Difficulty adjustment restriction is another way to say "something really bad or unusual has happened" and respond respectively.

I had checked ChatGPT and it did not produce the correct answer!

[promise444c5]

~

Absolutely learning.....

[Churchillvv]

I had checked ChatGPT and it did not produce the correct answer!

Well thanks for your lectures!

I also asked ChatGPT but I discovered it had no close answer so I did the math again and with a simple step some hours ago before checking here for the final answer, I discovered I was close to the final answer.

using the simple step; Old difficulty= 42
Currently block reward which is =     3.15

= 42 ÷ 3.125

my final answer came up as = 13.44 which is some how close to your final answer of 13.125.

Matching numbers where 13 but after the decimal it changed because I was not accurate with the formula.

once again thanks for the knowledge shared.

[hosseinimr93]

= 42 ÷ 3.125

Why did you divide the difficulty by the block reward?
The difficulty adjustment has nothing to do with the block reward. The difficulty is adjusted to maintain the average block time of 10 minutes.

my final answer came up as = 13.44 which is some how close to your final answer of 13.125.

Just a coincidence.

[Churchillvv]

= 42 ÷ 3.125

Why did you divide the difficulty by the block reward?
The difficulty adjustment has nothing to do with the block reward. The difficulty is adjusted to maintain the average block time of 10 minutes.

I don't really know  I guess that was my own interpretation of what I read although it's totally wrong but my instinct said I should share, and then clarification would be the result right ?

my final answer came up as = 13.44 which is some how close to your final answer of 13.125.

Just a coincidence.

I guess so, nothing more nothing more nothing less !

[Ambatman 2]

I had checked ChatGPT and it did not produce the correct answer!

Well thanks for your lectures!

I also asked ChatGPT but I discovered it had no close answer so I did the math again and with a simple step some hours ago before checking here for the final answer, I discovered I was close to the final answer.

using the simple step; Old difficulty= 42
Currently block reward which is =     3.15

= 42 ÷ 3.125

my final answer came up as = 13.44 which is some how close to your final answer of 13.125.

Recall the question said the current difficulty is halved (current is around 84 Trillion)
And using same block reward was the first flaw of the working.

I don't really know  Huh I guess that was my own interpretation of what I read although it's totally wrong but my instinct said I should share, and then clarification would be the result right ?

Yeah. It goes a long way in assisting self growth.
I think what you did is find the difficulty per reward in the question.

The trick of this quiz was the knowledge of difficulty adjustment restriction to a factor of 4, as shown in here: https://github.com/bitcoin/bitcoin/blob/4a020ca443ba370bf41583962d16aa8551876f53/src/pow.cpp#L54-L59. The reason we do not allow difficulty to grow beyond 300% or drop by less than 75%, is to achieve a middle ground between resilience in network disruption and quick response to a genuine change in the hashrate.

understanding codes isn't my strong suit
So didn't understand what's on the link much.
Was the 4 as a result of the fact that not less than 75% is 25% (100%-75%).
Where 25% is same as 1/4 which looks similar to hosseinimr93 solving
52.5*1/4 = 52.5/4 .

I don't know if what I did is correct but if it was, does that mean that if the reverse was the case and the block time of the current epoch is 1 hour and falls to 10 minutes.( using difficulty of 52.5 Trillion). 

Would the difficulty increase to 52.5 * 300%/100% =52.5 * 3 =157.5 Trillion.

Since trying 52.5*60/10 =315 T
Where 1 hour =60 min.

And the increment was (315-52.5)/52.5 *100%/1 = 500%
Which is greater than 300%.

[BlackHatCoiner]

understanding codes isn't my strong suit
So didn't understand what's on the link much.

It's two simple conditions:

Code:

if (nActualTimespan < params.nPowTargetTimespan/4)
        nActualTimespan = params.nPowTargetTimespan/4;\
if (nActualTimespan > params.nPowTargetTimespan*4)
        nActualTimespan = params.nPowTargetTimespan*4;

Beginning from the first, if it's true, meaning if "the actual timespan was less than only the quarter (25%) of the current timespan", then set it equal with the quarter, and don't go below. If the actual timespan is more than the quarter of the current (but not more than 4x the current), both these conditions will evaluate false and it will continue executing the code below, which will set the new difficulty based on expected / actual.

Edit:

I don't know if what I did is correct but if it was, does that mean that if the reverse was the case and the block time of the current epoch is 1 hour and falls to 10 minutes.( using difficulty of 52.5 Trillion).

Would the difficulty increase to 52.5 * 300%/100% =52.5 * 3 =157.5 Trillion.

If in the current epoch, we had 1 hour average block time, then expected / actual would be 20160 / 120960 = 0.166, which is less than 0.25, and therefore, with hashrate constant, it'd be impossible to drop to 10 minutes average block time in just one difficulty adjustment. We'd drop to 15 minutes first, and then to 10.

[EL MOHA]

using the simple step; Old difficulty= 42
Currently block reward which is =     3.15

= 42 ÷ 3.125

my final answer came up as = 13.44 which is some how close to your final answer of 13.125.

Matching numbers where 13 but after the decimal it changed because I was not accurate with the formula.

This is just merely a case of coincidence because the block reward has nothing to do with the difficulty of the network, if at all the block reward is been used it will be almost impossible to have a change In the difficult adjustment because the reward is fixed for 210000 blocks whereas the difficulty is adjusted every 2016 blocks with a new average time used, which is a huge difference.

[Amphenomenon]

I literally ignored the fact that the whole scenario did played till C, failed realize this earlier, sigh. Still got a long way to go.