The official Serenes Forest riddles

[Balcerzak]

[spoiler=magic square]

 8  3  4
 5  1  2
 7  9  6   

I'm not sure how to show my work on this one. I don't know that there's a deterministic solution, so I trialed and errored it.

[noiku]

8 + 3 + 4 = 15

+ + +

5 + 1 + 2 = 8

+ + +

7 + 9 + 6 = 22

= = =

20 13 12

Edited August 17, 2016 by Virtual Singer

[MarioKirby]

[spoiler=]

8 + 2 + 5 = 15

+ + +

3 + 4 + 1 = 8

+ + +

9 + 7 + 6 = 22

= = =

20 13 12

Also, regarding the last problem: I was getting the wrong answers because I misunderstood the wording. Oops.

[MisterIceTeaPeach]

All answers are correct.

Different results are possible in this case.

I couldn't find a pattern either tbh.

The only thing you have to keep in my mind to add low numbers in the addition with the lowest result and high numbers in the addition with the highest result.

Qustion 5: Stochastics

You play against the final boss in a Fire Emblem game. The opponent has 120 HP.

You attack it and the battle screen shows you these stats:

Damage: 4 x 12

Accuracy: 85%

Critchance: 25%

Unlike in the Fire Emblem series the RNG shall work different here. [spoiler=The accuracy and critchance depend on each other.]That means in this case that the critcance isn't 25% since the accuracy isn't 100%.

[spoiler=An example if you didn't understand the given explanation]

Attack 15

Accuracy 90%

Critchance 15%

Question: What is the % freqence ti land a critical hit?

Answer: You have to multiple the accuracy with the critchance: 0,9 x 0,15 = 0,135 => 13,5%

1. What is the % frequency to hit all four times?
2. What is the % frequency to land a critical hit?
3. What is the % frequency to kill the boss in one single phase?

(A calculator is recommended at least for 3.)

Edited August 18, 2016 by Ayama Wirdo

[noiku]

[spoiler=]

1. Rounded: 52% Non-rounded: 52.200625%

2. Rounded: 21% Non-rounded: 21.25%

3. Rounded: 11% Non-rounded: 11.0926328125%

[MisterIceTeaPeach]

[spoiler=]

1. Rounded: 52% Non-rounded: 52.200625%

2. Rounded: 21% Non-rounded: 21.25%

3. Rounded: 11% Non-rounded: 11.0926328125%

1. + 2. are correct!

[spoiler=3 isn't]

You have to keep in mind that the boss has 120 HP and that you need three critical hits and one regular hit (3x12x3 + 12 = 120) to beat it. The % possibility has to be extremly low.

Maybe it wasn't quite obvious: I meant with beating "onerounding" in one phase.

Edited August 18, 2016 by Ayama Wirdo

[noiku]

[spoiler=Question 3]

Rounded: 13% Non-rounded: 13.05015625

[Topazd]

Unlike in the Fire Emblem series the RNG shall work different here. [spoiler=The accuracy and critchance depend on each other.]That means in this case that the critcance isn't 25% since the accuracy isn't 100%.

[spoiler=An example if you didn't understand the given explanation]

Attack 15

Accuracy 90%

Critchance 15%

Question: What is the % freqence ti land a critical hit?

Answer: You have to multiple the accuracy with the critchance: 0,9 x 0,15 = 0,135 => 13,5%

Isn't that exactly how the RNG in FE works (barring 2RN), though?

Anyhow

1.

0,85^4 = ~52,2%

2.

If this means chance of critical on any given strike, 0,85*0,25 = 21,25%

If, however, you mean a single critical in a whole round of combat with four attacks, I put this together in Excel.

As the odds of landing a crit on the first strike are 21,25% (I'll arbitrarily call the odds of the attacks critting after the prior failing h_1-h₄₎, failing the first attempt, the odds of the second remedying that are (1-(h₁)*h₁, with the third looking like (1-(h₁₊h₂))*h₁ and the fourth one (1-(h₁₊h₂₊h₃))*h₁. Then h₁₊h₂₊h₃₊h₄ equals ~61,54%.

My formatting is probably ass but should get the point across, wanted to double-check it after the calc and at least Stat Trek's Binomial Calculator seems to validate it. P(X > 1) = odds of a critical proc at least once in 4 instances.

3.

With this I legitimately don't have any idea, haha. If you just go with 0,85*0,2125^3 you end up with roughly ~0,82% but I don't think that's the correct way to go about things. I'll probably check if the above calculator can shed any light on that afterwards.

I like the concept of this thread, have to say.

Edited August 18, 2016 by Topazd

[MisterIceTeaPeach]

[spoiler=Question 3]

Rounded: 13% Non-rounded: 13.05015625

Still way too high.

Isn't that exactly how the RNG in FE works (barring 2RN), though?

Anyhow

1.

0,85^4 = ~52,2%

2.

If this means chance of critical on any given strike, 0,85*0,25 = 21,25%

If, however, you mean a single critical in a whole round of combat with four attacks, I put this together in Excel.

As the odds of landing a crit on the first strike are 21,25% (I'll arbitrarily call the odds of the attacks critting after the prior failing h_1-h₄₎, failing the first attempt, the odds of the second remedying that are (1-(h₁)*h₁, with the third looking like (1-(h₁₊h₂))*h₁ and the fourth one (1-(h₁₊h₂₊h₃))*h₁. Then h₁₊h₂₊h₃₊h₄ equals ~61,54%.

My formatting is probably ass but should get the point across, wanted to double-check it after the calc and at least Stat Trek's Binomial Calculator seems to validate it. P(X > 1) = odds of a critical proc at least once in 4 instances.

3.

With this I legitimately don't have any idea, haha. If you just go with 0,85*0,2125^3 you end up with roughly ~0,82% but I don't think that's the correct way to go about things. I'll probably check if the above calculator can shed any light on that afterwards.

I like the concept of this thread, have to say.

Each result is correct.

(as for 2. I didn't say one crit of four times, otherwise it'd be exactly 85% (0,2125x4).

As for 3. it's absolutely no shame to do it on this way if you understood the concept, what you did as I can see. I use binomial distribution programs too.

About the RNG in FE: Idk how it works with the 2RN. People are talking about "true hit", but tbh I have no idea what it is exactly.

And I highly appreciate this compliment.

Thanks!

Edited August 18, 2016 by Ayama Wirdo

[Topazd]

(as for 2. I didn't say one crit of four times, otherwise it'd be exactly 85% (0,2125x4).

About the RNG in FE: Idk how it works with the 2RN. People are talking about "true hit", but tbh I have no idea what it is exactly.

That line of thought would lead to the odds of getting at least one crit within five attacks being 106,25% :p

This explains true hit pretty well. But what I meant by that was that the 'real' chance to critical depends on hit% in actual FE as well.

Edited August 18, 2016 by Topazd

[noiku]

[spoiler=]

Non-rounded: 00.815635%

[MisterIceTeaPeach]

That line of thought would lead to the odds of getting at least one crit within five attacks being 106,25% :p

This explains true hit pretty well. But what I meant by that was that the 'real' chance to critical depends on hit% in actual FE as well.

Thanks!

Oh, I understand now. Also how it's calculated

Anyways I prefer the system which was used in the first five parts. It's the most logical and obvious to understand.

[spoiler=]

Non-rounded: 00.815635%

Correct!

[Balcerzak]

What is the % frequency to hit all four times? (0.85)^4 (~0.522)

What is the % frequency to land a critical hit? (0.85*0.25) (~0.2125)

What is the % frequency to kill the boss in one single phase?

The boss's health is 120. A crit is 36 damage. 3 crits is 108 damage. The fourth hit will be enough regardless of if it crits or not. Therefore:

[(0.85*0.25)^3*(0.85)] (~0.00816)

[MisterIceTeaPeach]

What is the % frequency to hit all four times? (0.85)^4 (~0.522)

What is the % frequency to land a critical hit? (0.85*0.25) (~0.2125)

What is the % frequency to kill the boss in one single phase?

The boss's health is 120. A crit is 36 damage. 3 crits is 108 damage. The fourth hit will be enough regardless of if it crits or not. Therefore:

[(0.85*0.25)^3*(0.85)] (~0.00816)

Correct!

Also I'm going to do the next riddle tomorrow morning.

[MarioKirby]

[spoiler=]

1. - 52.200625%, or about 52%

2. - I'm assuming we're talking about the possibility of a single critical hit, which would be 21.25%, or about 21%

3. - In order to one-round the opponent, you need all four attacks to hit and at least three of them have to critical. Taking the precise percentages from earlier, that would be .815634765625%, or about a .82% chance; using the rounded percentages from earlier, it would be .787185%, or about .79%.

[Roxas]

What if we used supports and triangle attacks :<

[MisterIceTeaPeach]

[spoiler=]

1. - 52.200625%, or about 52%

2. - I'm assuming we're talking about the possibility of a single critical hit, which would be 21.25%, or about 21%

3. - In order to one-round the opponent, you need all four attacks to hit and at least three of them have to critical. Taking the precise percentages from earlier, that would be .815634765625%, or about a .82% chance; using the rounded percentages from earlier, it would be .787185%, or about .79%.

I assume in 3. you left out the 0 before the dezimal point, so all answers are correct.

What if we used supports and triangle attacks :<

Boss has FE4 nihil and FE9 parity.

[spoiler=Calculation for a triangle attack]

(0,85*0,25)²*0,85=0,038=>3,8%

Question 6: Geometry

A right-angled triangle ABC is given.

One cathetus is 1cm longer than the other one and 1cm shorter than the hypotenuse.

1. How long are the catheti and the hypotenuse?
2. How much ° do the two other angels ammount?
3. How large is the surface area of this triangle?

Edited August 19, 2016 by Ayama Wirdo

[MisterIceTeaPeach]

1. catheti- 3 and 4 hypotenuse- 5

2. 30 and 60 degrees

3. 12

[spoiler=This was fast!]

1. + 2. are correct. For 3. you calculated the surface are for a rectangle. For a triangle you have to halve your result, so it's 6.

[MarioKirby]

[spoiler=]

1. the side lengths are 3 cm for the smaller cathetus, 4 cm for the longer cathetus, and 5 cm for the hypotenuse.

2. Are we talking about both angle measures individually or the total of the two? The total would be 90 degrees, as a triangle has a total interior angle measure of 180 degrees, and the right angle accounts for 90 degrees of it. If it's the measures of each angle specifically, then I'll post later with those, as I haven't figured those at the time of posting.

3. the surface area would be 6 cm².

[Balcerzak]

1) 3 cm, 4 cm, 5 cm

2) arcsin (4/5) and arcsin (3/5)

3) 6 cm^2

[MisterIceTeaPeach]

[spoiler=]

1. the side lengths are 3 cm for the smaller cathetus, 4 cm for the longer cathetus, and 5 cm for the hypotenuse.

2. Are we talking about both angle measures individually or the total of the two? The total would be 90 degrees, as a triangle has a total interior angle measure of 180 degrees, and the right angle accounts for 90 degrees of it. If it's the measures of each angle specifically, then I'll post later with those, as I haven't figured those at the time of posting.

3. the surface area would be 6 cm².

1. +3. are correct.

As for 2 you have to figure out the angle of the two catheti. 90° for the two angles remain.

1) 3 cm, 4 cm, 5 cm

2) arcsin (4/5) and arcsin (3/5)

3) 6 cm^2

Correct!

Edited August 19, 2016 by Ayama Wirdo

[MarioKirby]

[spoiler=]

Then the angles are 36.87 degrees and 53.13 degrees for the smaller and larger angle, respectively, rounded to the nearest hundredth.

[MisterIceTeaPeach]

[spoiler=]

Then the angles are 36.87 degrees and 53.13 degrees for the smaller and larger angle, respectively, rounded to the nearest hundredth.

It's correct.

Question #7: Perfect number

I found this question quite interesting:

Tbh it's the first time I've heared about the term "perfect number".

Tell the first two positive numbers which are a perfect number.

Edited August 20, 2016 by Ayama Wirdo

[Rezzy]

[spoiler=Guess]6: 1,2,3,6
28: 1,2,4,7,14,28

Julian, you must be up either really late or really early.

Edited August 20, 2016 by Rezzy

[MisterIceTeaPeach]

[spoiler=Guess]6: 1,2,3,6

28: 1,2,4,7,14,28

Julian, you must be up either really late or really early.

It's correct.

Tbf I still have memorized these numbers from this question.

I came up with this question after I had got up. I guess 6:50 AM is pretty early already.

Sry, but I've a different bedtime than most other people here.

Also you can submit all the answers of the previous questions.

I would check them all.

2. 30 and 60 degrees

Sry for seeing too late, but this answer is also incorrect.

Edited August 20, 2016 by Ayama Wirdo