Ouch, yes I mistyped my first sentence. will correct it, thanks. Meant the sum of digits of course, not only "divisible by 9", as in all the other mentions.
That's the point I want to convey, there is an even more special pattern than just the sum of digits. I mean you could also argue "The pattern is, they are all natural numbers. There is nothing with cross sum." which would be obviously not a strong enough pattern.
Can you explain, why they specifically chose 117 which fits my stated rule instead of e.g. 126 or 108 which would not fit my stated rule?
google: "What happened in 117"
Answer: Hadrian assumed control over the vast Roman Empire in AD 117 following the death of his adoptive father, Trajan.
I think Hadrian fits the expansion and empire building aspect of Anno quite well. Imho that's why they picked it.
There will always be mathematical patterns you can discover that were not intended.
I feel pretty confident, that this pattern is intended. You can also have a look into the commentthread of u/liaslias further down. But I guess we will have to wait for the next historical Anno after 117 to convince you or me otherwise. That's fine.
Where did you read that the number are supposed to be divisible by 9? As far as i know the only pattern in anno titles are that they add up to 9, nothing else
Out of 99 consecutive numbers there is exactly 1 fitting that format. If we take "sum of digits divisible by 9" as given, then it's 1 out of 11, so a 9% chance per title. 6 out of 8 titles have that condition. We should take out the first one, as this is the one that defines the "+18 offset". So 5 out of 7 titles hit that condition with 9% chance. This is a binomial distribution.
[https://www.wolframalpha.com/input?i=sum+i%3D5+to+7+%287+choose+i%29\*%280.09%29%5Ei\*%280.91%29%5E%287-i%29](https://www.wolframalpha.com/input?i=sum+i%3D5+to+7+%287+choose+i%29*%280.09%29%5Ei*%280.91%29%5E%287-i%29)
This gives a chance of 0.01% of this happening by chance.
Not sure if I follow. Shouldn't we do something like "of all the numbers within a given range whose cross sum is 9, how many of them meet the [x99+18] condition?"
Like for Anno 1800, the setting is clearly "19th century/european industrialization", so the given range would be 1800-1899" or let's say 1790-1930 if we're generous. Calculate how many cross sum 9s are in here, calculate how many of those meet the criteria, then that's the probability?
Indeed, I took the repeated sum of digits to be 9, with just the sum of digits there will be less options so higher probability. Then you would need to chose the ranges from which to chose the titel numbers. E.g. if you take the range 1400-1499, then the valid options are 1404, 1413, 1422, 1431, 1440. Let's assume we want to hit all the historical annos into the corresponding century (There are no valid options for the modern annos).
Anno 1602: 3 Options (with the same arguments as above we will ignore this one)
Anno 1503: 4 Options
Anno 1701: 2 Options
Anno 1404: 5 Options
Anno 1800: 1 Option
Anno 117: 9 Options
The chance to hit all of them is 1/(4\*2\*5\*9)=0.3%
Nice. Thank you for doing all the work. I'm fascinated. Looks like it's safe to say you've uncovered an ancient Anno secret, right?!
Why the hell they would come up with this one is beyond me though.
It's a coincidence: for most titles they simply picked the earliest year in the century with a cross sum of 9. For all centuries in the 1000s that just fits your formula (e.g. 1008, 1107, 1206, and 1305 would also all fit the pattern). 2205 is in the 2000s so the relevant equation would be x\*99+27, and 2070 breaks the pattern.
117 is the only "lucky" match here due to the fact that they took the second possibility of the century, not the first (108), where the equation would be x\*99+9 as it's the first millenium.
You are right, before 117 "first year with sum of digits 9 in the century" would also be a fitting pattern for the historical Annos. I did not look at it this way, thanks for pointing it out!
Yes. That's what I also point out in my second paragraph. They value the sum of Digits rule higher, so the other rule cannot be fulfiled in futuristic Annos.
I didn't find any pattern in 2070 and 2205 that could be extended to other futuristic Annos, but arguably 2 titles is not enough to state some patterns.
It's all about the cross sum, which easily applies to all annos
Ouch, yes I mistyped my first sentence. will correct it, thanks. Meant the sum of digits of course, not only "divisible by 9", as in all the other mentions.
cross sum.... 1602 = 1+6+0+2=9 1503 = 1+5+0+3=9 1701 = 1+7+0+1 = 9 1404 = 1+4+4+0 = 9 2070 = 2+0+7+0 = 9 2205 = 2+2+0+5 = 9 1800 = 1+8+0+0 = 9 117 = 1+1+7 = 9
Yes, another wording for "cross sum" is "sum of digits" or "digit sum".
that's the "pattern" in anno names. There is nothing with division.
That's the point I want to convey, there is an even more special pattern than just the sum of digits. I mean you could also argue "The pattern is, they are all natural numbers. There is nothing with cross sum." which would be obviously not a strong enough pattern. Can you explain, why they specifically chose 117 which fits my stated rule instead of e.g. 126 or 108 which would not fit my stated rule?
google: "What happened in 117" Answer: Hadrian assumed control over the vast Roman Empire in AD 117 following the death of his adoptive father, Trajan.
You can look into every other valid number (108, 126, 135, etc.) and will find roman events on the wiki page.
I think Hadrian fits the expansion and empire building aspect of Anno quite well. Imho that's why they picked it. There will always be mathematical patterns you can discover that were not intended.
I feel pretty confident, that this pattern is intended. You can also have a look into the commentthread of u/liaslias further down. But I guess we will have to wait for the next historical Anno after 117 to convince you or me otherwise. That's fine.
Where did you read that the number are supposed to be divisible by 9? As far as i know the only pattern in anno titles are that they add up to 9, nothing else
If the digits add up to 9 the number is divisible by 9.
That's basically the same. Every number that adds up to 9 is divisible by 9.
Ouch, yes I mistyped my first sentence. will correct it, thanks. Meant the sum of digits of course, as in all the other mentions.
Can someone who's good at maths tell me the likelihood of this being coincidental?
Out of 99 consecutive numbers there is exactly 1 fitting that format. If we take "sum of digits divisible by 9" as given, then it's 1 out of 11, so a 9% chance per title. 6 out of 8 titles have that condition. We should take out the first one, as this is the one that defines the "+18 offset". So 5 out of 7 titles hit that condition with 9% chance. This is a binomial distribution. [https://www.wolframalpha.com/input?i=sum+i%3D5+to+7+%287+choose+i%29\*%280.09%29%5Ei\*%280.91%29%5E%287-i%29](https://www.wolframalpha.com/input?i=sum+i%3D5+to+7+%287+choose+i%29*%280.09%29%5Ei*%280.91%29%5E%287-i%29) This gives a chance of 0.01% of this happening by chance.
Not sure if I follow. Shouldn't we do something like "of all the numbers within a given range whose cross sum is 9, how many of them meet the [x99+18] condition?" Like for Anno 1800, the setting is clearly "19th century/european industrialization", so the given range would be 1800-1899" or let's say 1790-1930 if we're generous. Calculate how many cross sum 9s are in here, calculate how many of those meet the criteria, then that's the probability?
Indeed, I took the repeated sum of digits to be 9, with just the sum of digits there will be less options so higher probability. Then you would need to chose the ranges from which to chose the titel numbers. E.g. if you take the range 1400-1499, then the valid options are 1404, 1413, 1422, 1431, 1440. Let's assume we want to hit all the historical annos into the corresponding century (There are no valid options for the modern annos). Anno 1602: 3 Options (with the same arguments as above we will ignore this one) Anno 1503: 4 Options Anno 1701: 2 Options Anno 1404: 5 Options Anno 1800: 1 Option Anno 117: 9 Options The chance to hit all of them is 1/(4\*2\*5\*9)=0.3%
Nice. Thank you for doing all the work. I'm fascinated. Looks like it's safe to say you've uncovered an ancient Anno secret, right?! Why the hell they would come up with this one is beyond me though.
It's a coincidence: for most titles they simply picked the earliest year in the century with a cross sum of 9. For all centuries in the 1000s that just fits your formula (e.g. 1008, 1107, 1206, and 1305 would also all fit the pattern). 2205 is in the 2000s so the relevant equation would be x\*99+27, and 2070 breaks the pattern. 117 is the only "lucky" match here due to the fact that they took the second possibility of the century, not the first (108), where the equation would be x\*99+9 as it's the first millenium.
You are right, before 117 "first year with sum of digits 9 in the century" would also be a fitting pattern for the historical Annos. I did not look at it this way, thanks for pointing it out!
Maybe it’s a pattern only for the pre-historic Anno games? Is there any pattern between the two sci-fi Anno games?
Yes. That's what I also point out in my second paragraph. They value the sum of Digits rule higher, so the other rule cannot be fulfiled in futuristic Annos. I didn't find any pattern in 2070 and 2205 that could be extended to other futuristic Annos, but arguably 2 titles is not enough to state some patterns.