What are my coincidences?

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I wrote "GmbH" (German abbreviation) and "you just see an apple" (English phrase) before writing sentence "Kot mruczy, a krowa muczy" ("Cat purrs, and cow moos"), words "Grodno" (large city in western Belarus) and "Kowno" (Kaunas, second largest Lithuanian city) and the word "krowno" (my neologism for cow excrement). The sentence "Kot - po niemiecku znaczy to "kał"" ("Kot - in German it means "feces"") was also written. It was 16.4.2018.

The date 16.4.2018 has a rare property because from it five natural powers of number two can be separated: 16, 4, 2, 1, 8. And "number two" is slang or childish term for feces and coincidence was in large part associated with feces. Polish word "kał" ("feces") has similar pronunciation as English word "cow" ("krowa" in Polish). And Polish word for cat means feces in German (where it starts with capital letter because it is a noun). The date 18.4.2016 also gives such an effect. 18.4.2016 I started third week in day hospital (oddział dzienny in Polish).

Both dates: 16.4.2018 and 18.4.2016 have 4, 6, 8 as last digits in numbers forming them. So there is also coincidence with 3, 6, 9 because numbers 4, 6, 8 also form three-membered arithmetical sequence with sum 18 and arithmetical mean 6. In addition, 4, 6, 8 are one-digit numbers. Similarly coincident date is 4.6.2018 (when I was diagnosed with F84.5, F42.2, F21 at the visit with the psychiatrist), which has sum of digits 21 and from digits different than 4, 6, 8 numbers 21 and 210 (2*3*5*7, product of four one-digit prime numbers) can be formed.

Today I looked at Google results for certain four-lettered word written from Russian letters and there were 3 970 results. Next I looked for certain Russian phrase and there were 3 970 000 results. 1000 times more! Both phrases were associated with feces. Yesterday I wrote something about feces in that topic.

Some time ago I typed certain Russian phrase which was a transliteration of Russian name of certain creature from certain Russian game in which the encounter with Big W was present. In second or first result there was English name for the item called V in my earlier posts in that topic and two transliterations of Russian term for V! Today I typed that phrase again and there were no words for V.

Well...there you go!

For the first time you have actually found a real, and meaningful, coincidence!

The fact that both phrase were "associated with feces" is prove positive that God was trying to tell you something!

Tell you that all of this number stuff of yours is all a bunch of ….you know what!

A bunch of... yhhm... feces? I do not think so

24.12.2018 I noticed that from the digits of GS 21, 42, 84 two three-membered arithmetical sequences can be formed: 2, 8, 14 and 4, 8, 12. These ASes can be formed by digits of GS 1, 2, 4, 8.
1, 2, 4, 8 is a four-membered geometrical sequence. It is non-constant and has four digits in it. That GS can be formed by some digits of GS 21, 42, 84 and by some digits in numbers in the date 24.12.2018.

Large coincidence can be found in numbers formed by two last digits in numbers forming the date 24.12.2018. These numbers are: 24, 12, 18. If they are sorted ascendingly, they form an AS: 12, 18, 24. Sums of digits in numbers forming AS 12, 18, 24 are: 3, 9, 6, if they are sorted ascendingly, they form "Tesla's arithmetical sequence" (TAS) - 3, 6, 9!

1. Middle term in the sequence 12, 18, 24 is 18.
2. Arithmetic mean of the AS 12, 18, 24 is 18 ((12+18+24):3 = 54:3 = 18).
3. Sum of digits in numbers forming 12, 18, 24 is 18 (1+2+1+8+2+4 = 18).
4. Sum of products of digits in numbers forming 12, 18, 24 is 18: 1*2 + 1*8 + 2*4 = 2+8+8 = 18.

The GS 12, 18, 24 is very coincident with sum of numbers and digits in TAS - 18. It may be the only non-constant sequence which has the same arithmetical mean, sum of digits and sum of products (or only digits which are present in the numbers) of digits in numbers forming the sequence. Another example of such a sequence is constant 0,0,0.

The common difference of 12, 18, 24 is 6 - the same as CD of 6, 12, 18, which was also coincident because 6.12.2018 I noticed that product of digits in the AS 11, 15, 19 is the same as sum of numbers forimng that sequence. 6 is arithmetical mean and middle term of TAS. Both 6, 12, 18 and 11, 15, 18 have the same sum of digits - 18, the same as in the case of TAS.

There are 9 days between 6.12.2018 and 15.12.2018 and 9 days between 15.12.2018 and 24.12.2018. There are 18 days between 6.12.2018 and 24.12.2018.

I noticed coincidences associated with 3, 6, 9 and 21.7 associated with the arithmetic sequence (AS) 6, 13, 20. They look amazing.

1. Sum of digits in 6, 13, 20 is 12 (21 read backwards, 3+9) and sum of numbers is 39 (number starting on 3 and ending on 9, just like 3, 6, 9, in addition, arithmetic mean of digits in 39 is 6).
2. First digits in that sequence have sum 9 (6+1+2) and second digits have sum 3 (3+0). Arithmetic mean (AM) of 9 and 3 is 6, difference of 9 and 3 is also 6.
3. Product of 3, 6, 9 (162) can be formed from first digits of numbers in 6, 13, 20. Product of 21 and 6 (126, having the same digits as two factors) also can be formed from these numbers.
4. Common difference of AS 6, 13, 20 is 7 and number 21 can be formed from digits forming that sequence.
5. Three-membered geometric sequence (GS) with sum 21 and AM 7 can be formed from digits of 6, 13, 20: 3, 6, 12. Sum of digits in that GS is 12 and it is 3 times smaller than the product of digits forming that sequence (3*6*1*2 = 36).
6. A three-membered AS with sum 3 can be formed from 6, 13, 20: 0, 1, 2.
7. A three-membered AS with sum 6 can be formed from 6, 13, 20: 1, 2, 3.
8. A three-membered AS with sum 9 can be formed from 6, 13, 20: 0, 3, 6.
9. Two three-membered ASes with sum 18 (3+6+9) and AM 6 (the same as in 3, 6, 9) can be formed from 6, 13, 20: 0, 6, 12 and 2, 6, 10. It is big coincidence!
10. From digits other than 6 in the sequence 6, 13, 20 four-membered AS can be formed (0, 1, 2, 3), it has the sum 6.
11. From five digits of 6, 13, 20 another three-membered AS consisting of five digits and three numbers can be formed: 0, 16, 32. It has the sum 48 and arithmetic mean of digits in 48 is 6, in addition 48-39 is 9 (39 is the sum of numbers in "original" sequence 6, 13, 20).

I typed phrase associated with transliteration of certain Russian phrase and with certain Russian computer game. In the description of 9th result (that which was at the lowest part on first page of results) I found letter "V"! Песни на букву «V» - OriginSound.ru - that was the description. Earlier I read or typed in Google something about "bukva r" (Russian word for "letter r"). "V" was associated with the Russian game.

I typed names of two items found in coincident encounter in which "V" was found - one phrase, without quotation marks, two words. There were 246 000 000 results. 2, 4, 6 - numbers form an arithmetic sequence, in addition, they are the same as sums of digits in the sequences: 6, 13, 20 (sums of digits have to be sorted ascendingly to form 2, 4, 6) or 11, 13, 15 (these two ASes were coincident earlier). These two short names have the same number of letters in them and the same two first letters.

Today I typed three phrasese in Google and there were interesting numbers of results:
- for orojenia (modification of Polish word "urojenia" meaning delusions) there were 112 results,
- for grzech dotykanie żony (sin touching of wife) there were 112 000 results,
- for sadis there were 11 200 000 results.
112 is the product of numbers 28 and 4. I was diagnosed with F21, F42.2, F84.5 together first time 28.4.2015.

I also typed the word swinemeat and results for swine meat were presented. There were 17 400 000 results. From digits of 17 4 the number 147 can be formed, 147 is 21*7.
I typed a word associated in some way with certain creature from certain game. There were 14 700 results.
I typed certain three-lettered word and got 65 700 000 results. Numbers: 6, 5, 7 sorted ascendingly form arithmetic sequence with sum 18 and arithmetic mean 6, just like 3, 6, 9.
I typed Polish name of "Big W" encounter mentioned earlier. There were 5 880 000 results. Sum of digits 5, 8, 8 is 21 and arithmetic mean is 7.
I typed Polish name of something unpleasant and got 87 300 results. Sum of digits 8, 7, 3 is 18 and arithmetic mean is 6.
I typed certain phrase in Google and there were 28 400 000 results. 28 and 4! 28.4.

I noticed that from digits of sequence 33, 42, 51 four other arithmetic sequences (which have arithmetic mean 33) can be formed:
- 12, 33, 54 (common difference 21)
- 21, 33, 45 (common difference 12)
- 25, 33, 41 (CD
- 14, 33, 52 (CD 19).
Interestingly, it is not the only set of four numbers with sum of digits 18 which has such a property. Another four arithmetic sequences with such common differences are formed from digits: 1, 2, 2, 3, 4, 6:
- 21, 42, 63 (CD 21)
- 12, 24, 36 (CD 12)
- 23, 42, 61 (CD 19)
- 16, 24, 32 (CD .
I found also a set of four arithmetic sequences with sums of digits 15 which has such CDs:
- 15, 23, 31 (CD
- 13, 32, 51 (CD 19)
- 11, 32, 53 (CD 21)
- 11, 23, 35 (CD 12).

In my previous post there were emoticons instead of number 8 and quotation mark.

From digits of numbers: 6, 13, 20 (0, 1, 2, 3, 6) many ascending arithmetic sequences can be formed:
1. 0, 1, 2 (sum 3, arithmetic mean (AM) 1, common difference (CD) 1)
2. 1, 2, 3 (sum 6, AM 2, CD 1)
3. 0, 1, 2, 3 (sum 6, AM 1,5, CD 1)
4. 0, 3, 6 (sum 9, AM 3, CD 3)
5. 0, 6, 12 (sum 18, AM 6, CD 6)
6. 2, 6, 10 (sum 18, AM 6, CD 4)
7. 0, 13, 26 (sum 39, AM 13, CD 13)
8. 6, 13, 20 (sum 39, AM 13, CD 7)
9. 0, 16, 32 (sum 48, AM 16, CD 16)
10. 0, 31, 62 (sum 93, AM 31, CD 31)
11. 2, 31, 60 (sum 93, AM 31, CD 29)
12. 2, 16, 30 (sum 48, AM 16, CD 14)
Interestingly, all three-digit or four-digit sequences (there are 6 such sequences) have sum of numbers 3, 6, 9 or 18. 18 is the sum of numbers: 3, 6, 9. There are two sequences with sum 6 (and 6 is arithmetic mean of 3, 6, 9 sequence) and two sequences with sum 18. There are 3 three-digit sequences, 3 four-digit sequences and 6 five-digit sequences.
In addition, sequences with sum 18 are interestingly associated with 3, 6, 9:
- they have three terms,
- they have six as their arithmetic mean and middle member,
- they have nine as their sums of digits.

From digits of 6, 13, 20 a geometric sequence (ascending) can be formed:
3, 6, 12.
That sequence has sum of numbers 21 and arithmetic mean 7!
Differences between the terms of that sequence are also interesting:
- difference of middle and the smallest term is 3 (6 - 3),
- difference of the largest and middle term is 6 (12-6),
- difference of the largest and the smallest term is 9 (12-3).
Amazing! That sequence is coincident with both 21.7 and 3, 6, 9.

At the beginning of that month I had large coincidence associated with buying paroxetine-containing medication.

1. It was 1.2.2019.
2. I paid 11,73 PLN.
3. I bought 3 packages of drug, 30 tablets in each, one tablet contains 20 mg of paroxetine.

The coincidence is associated mainly with numbers:
- 21.7,
- 3, 6, 9
- 21, 42, 84.

From digits of price of three packages two ascending arithmetic sequences with sums of numbers 21 and arithmetic means 7 can be formed:
- 1, 7, 13
- 3, 7, 11.
These sequences are formed by non-composite numbers.

Product of digits in number 11,73 is 21 (1*1*7*3 = 21).
Product of digits in number 11 is 21 times smaller than product of digits in number 73.
Arithmetic mean of numbers 11 and 73 is 42.
Sum of numbers 11 and 73 is 84.

One package of medication has 30 tablets.
30 tablets contain about 600 mg of paroxetine.
3 packages contain 90 tablets.
90 tablets contain about 1800 mg of paroxetine.
Digits which are not zeros form numbers: 3, 6, 9, 18 (18 is the sum of 3, 6, 9).
In these results of multiplication there were one or two zeros. Two times one zero, two times two zeros. There is a zero in the date 1.2.2019 and two numbers 2 and two numbers 1.

We have three numbers associated with the medication: 30, 20 and 3. Let's multplicate two of them:
30*20 = 600
20*3 = 60
30*3 = 90
In all three multiplications at least one number 3 was present.
Digits in products which are other than zeros are all from 3, 6, 9 group (namely 9 and two 6s). There are three digits: 9, 6, 6. Their sum is... 21 and arithmetic mean is... 7!

From digits in the date 1.2.2019 three-membered arithmetic sequence with two-digit numbers can be formed:
- 19, 20, 21.
Number 19 is quite important for me. One of my first large coincidences was associated with events from 19.9.2014, from that date two numbers 19 can be formed. 19 has also "private" meanings for me.
Number 20 is associated with amount of paroxetine in one tablet in medication which was bought. It is also the arithmetic mean of the sequence: 19, 20, 21.
Number 21 is "notoriously" coincident for me. Two numbers 21 can be formed from digits of the date: 1.2.2019.

One of my first coincidences was associated with three biggest Abrahamic religions: Christianity, Islam, Judaism. It happened 19.9.2014. I photographed Jewish cementery with matzevahs with Hebrew letters and a part of Catholic cementery with crosses. It was that day of the week during which Crucifixion of Christ happened and which is considered the rest day by many Muslims. It was 19th day of the month which is dedicated to Holy Cross in Catholic religion. Two numbers 19 can be formed from the digits of the date 19.9.2014. I read before starting of the coincidences that 19 is "special" number for some Muslims. About 11 p.m. I used the smartphone which was used to make the photographs of cementeries to watch posts written by another individual who was diagnosed with Asperger's syndrome. On some of posts which I saw 19.9.2014 Catholic or Jewish cementeries were present (with crosses or matzevahs with Hebrew letters, respectively). I saw one post from 19.7.2013 (in summer time), which was the youngest of posts in which that person with ASD wrote about cementeries.

Today I noticed that in date 19.7.2013 are the same digits like in the date 7.3.2019 (today). They are: 0, 1, 2, 3, 7, 9.
Five largest numbers (except zero) are highly coincident for me. From digits: 1, 2, 3, 7, 9 four-membered arithmetic sequence (AS) can be formed! It is: 1, 3, 9, 27. Quotient - 3.
Four largest numbers (except zero and one) are also coincident. From digits: 2, 3, 7, 9 three-membered AS can be formed: 3, 9, 27. Its sum is 39 and arithmetic mean is 13. Sum of digits in that sequence is 21 and arithmetic mean of sums of digits in these three numbers is 7!

I had coincidences with numbers associated with certain book. I read about some of them in second half of 2017. It looks dangerous for my religion! But I had coincidences with it. It looks from the biblical perspective that Quran was written by demons, I do not want to promote heresies, but I had quite many coincidences with something considered miracles (especially numerical, mathematical) of the book which is considered holy by Muslims. I read a lot about Quran's miracles (and knew about some of them before IX 2014) last time, I admit that they can look impressive, but belief in infallibility of Bible do not allow to consider Quran as final book from The Almighty. It is interesting why I have many coincidences with numerical miracles of Quran. I may have ideas that I have to spread knowledge about its mathematical miracles to the entire world and that I will destroy Christianity due to numerical miracles of Quran. I do not want to deprave anyone! It looks very bad and dangerous. Something like combination of reference, grandiose and messengership delusions.

So first coincidence with Quran mathematical miracles was associated with the triplets:
- 7, 29, 139 (numbers of: verses, words and letters in first surah),
- 7, 11, 13 (sums of digits in numbers forming triplet 7, 29, 139)
- 7, 2, 4 (sums of digits in sums of digits in numbers 7, 29, 139).

First triplet:
- three numbers,
- six digits,
- only one digit occurs two times and that digit is 9,
- from first digits of the numbers in 7, 29, 139 phrase "21 7" can be formed,
- sum of digits other than 2, 1 and 7 (9, 3, 9) is 21 and arithmetical mean of these three digits is 7 (again coincidence with 21 7),
- product of six digits forming that triplet is divisible by 7 and 21 or 3, 6, 9; it is 3402 (21*3*6*9).

Five "sorts" of digits are found in triplet 7, 29, 139: 1, 2, 3, 7, 9. Number 12379 is a prime.

I found four arithmetic sequences with prime numbers as extreme members and common differences which are formed by the same digits (in the sequences are present such digits: 1, 1, 2, 3, 4, 7):
11, 24, 37 (CD 13),
11, 42, 73 (CD 31),
13, 42, 71 (CD 29),
17, 24, 31 (CD 7).

1. Sums of numbers in these sequences are 72 or 126, the same as in three-membered arithmetic sequences with middle terms 24 or 42 formed from digits: 1, 2, 3, 3, 4, 5.
2. Arithmetic means in four sequences above are 24 or 42, just like in three-membered arithmetic sequences with middle terms 24 or 42 formed from digits: 1, 2, 3, 3, 4, 5.
3. Sums of extreme members in four sequences above are 48 or 84, just like in three-membered arithmetic sequences with middle terms 24 or 42 formed from digits: 1, 2, 3, 3, 4, 5.
4. Sums of digits in numbers forming four sequences mentioned above form ASes with sum of numbers 18 and arithmetic means of these numbers 6 - the same is in the case of "Tesla's arithmetic sequence" (3, 6, 9) and the sequence 33, 42, 51.
5. Sums of numbers in these four sequences divided by arithmetic means of sums of digits in numbers forming four sequences above are 12 or 21, like in the case of sequences: 15, 24, 33; 33, 42, 51; 13, 24, 35; 31, 42, 53 and 12, 24, 48; 21, 42, 84.
6. Sums of numbers in these four sequences divided by sums of digits in numbers forming four sequences above are 4 or 7, like in the case of sequences: 15, 24, 33; 33, 42, 51; 13, 24, 35; 31, 42, 53 and 12, 24, 48; 21, 42, 84.
7. There are 3 numbers in all of four ASes and these four sequences have 6 digits in any of them.

So these four sequences are in some way coincident to 21.7; 3, 6, 9 and 21, 42, 84. Large coincidence. 21.7 and 3, 6, 9 may look as the keys for many coincidences.

In four sequences above five "sorts" of digits appears. They are: 1, 2, 3, 4, 7. 12347 is an additive prime number.

15.4.2019 I have large coincidence associated with four five-digit three-membered ascending arithmetic sequences (ASes) formed by five of digits from that date. Almost year ago, in the same day of week, 16.4.2018, I had another large coincidences associated with something which I wrote in the notebook.

These four sequences are:
- 5, 12, 19 (common difference 7),
- 9, 12, 15 (CD 3),
- 1, 15, 29 (CD 14),
- 9, 15, 21 (CD 6).
Two first sentences were quite well known to me before 15.4.2019, I noticed that two with arithmetic means (AMs) 15 also can be formed by digits 1, 1, 2, 5, 9 at 15.4.2019, maybe at least in the case of 1, 15, 29 it was my first noticing it in my life.

Product of CDs of ASes with AMs 12 is 21 (7*3). 7 is the smallest number in the phrase "21 7" and 3 is the smallest number of AS 3, 6, 9.
Product of CDs of ASes with AMs 15 is 84 (14*6). 14 is arithmetic mean of numbers 21 and 7 and 6 is AM of numbers 3, 6, 9.

Extreme terms of the sequence 9, 15, 21 are the largest numbers in the phrases: 21 7 (21) and 3, 6, 9 (9).

Product of 21 and 84 is 1764, which is 42*42. 42^2 is also the product of products of arithmetic means and smallest numbers in phrases: 21 7 (AM 14, smallest number in the phrase 7, product of these two - 98) and 3 6 9 (AM 6, smallest number in the phrase - 3, product of these two - 18).

I had next large coincidence with three very coincident phrases:
- 21 7
- 3, 6, 9
- 21, 42, 84.

I had another coincidence with alleged numerical miracles in islamic scripture last times. I found such a page: https://pl.scribd.com/document/36754980 ... -Primalogy. On it such a text can be found:

So the Quran looks like a masterpiece of the fallen angels for a Christian...

This text is very coincident with:
- 2, 5, 11, 23, 47 (first five Thabit numbers which are additive primes, they are known for me since XI 2018);
- 27.4.2017;
- 24.7.2017;
- 11, 23, 47, 83, 131, 191, 263 (sequence of 7 additive prime numbers with additive primes being three first Thabit numbers as the sums of digits).

Almost all bolded numbers (23, 11, 797, 10037, 79733710037, 11171) in the text mentioned above are additive primes with additive primes being Thabit numbers as their sums of digits!
There is only one exception - 337, which has non-additive prime 13 as the sum of digits.
3, 7, 13 are three numbers associated with number 337 (its digits and sum of digits), sum of these three numbers is 23 - Thabit prime with another Thabit prime as sum of digits.
In addition, 13 is the sum of 1st and 3rd Thabit number - 2+11.
Two dates from 2017 are coincident with numbers 2, 11 and 23. 27.4.2017 and 24.7.2017 have sums of digits 23 and have sums of numbers being 2048. 2048 is 11th power of 2 (2^11)! What is more, the date in the text is Nov 2nd, 2017 - 2.11.2017! Numbers 2 and 11 again! In addition, two (2) numbers 11 can be formed from digits of last bolded number in the text above (from digits of 11171)! Amazing!

I noticed that in the decade 2011 - 2020 there were 21 dates with all six digits: 0, 1, 2, 3, 7, 9 in them. These six digits are present at least once in prime numbers bolded on the slide about chapters of Quran with prime numbers as sums of words in them.

These dates are:
* in 2013 (6 dates):
1. 09.07.2013
2. 19.07.2013
3. 29.07.2013
4. 07.09.2013
5. 17.09.2013
6. 27.09.2013
* in 2017 (7 dates):
1. 09.03.2017
2. 19.03.2017
3. 29.03.2017
4. 03.09.2017
5. 13.09.2017
6. 23.09.2017
7. 30.09.2017
* in 2019 (8 dates):
1. 07.03.2019
2. 17.03.2019
3. 27.03.2019
4. 03.07.2019
5. 13.07.2019
6. 23.07.2019
7. 30.07.2019
8. 31.07.2019

Numbers of dates in years form arithmetic sequence: 6, 7, 8, which has sum 21 and arithmetic mean 7.

On one page mentioned earlier there were seven numbers which were bolded (bolded by me below have not Thabit number as the sum of digits, underlined have not Thabit numbers as the number of digits in them):
- 23
- 11
- 797
- 10037
- 337
- 79733710037
- 11171
Most of numbers above are not only additive primes, but also have Thabit numbers as the sum of digits (6 of 7) and Thabit number as number of digits (5 of 7).

Let's look at the only number which has not 321 number (another term for Thabit number) as the sum of digits - 337:
1. There is one digit which occurs only once in that number - 7.
2. There is one digit which appears more than one time - it is 3.
3. Product of 3 and 7 (single digits occurring in number 337) is 21 and sum is 10 (which is the same sum as in the case of 21 7).
4. Number of digits in number 337 is 3.
5. Sum of digits which repeat themselves is 6 (3+3).
6. Product of digits which repeat themselves is 9 (3*3).
7. Product of all three digits in 337 is divisible by 7 and 21 and it is 63.
8. In number 63 occurs only digits 6 and 3, sum of digits in 63 is 9.
9. Product of digits in number 63 is 18, which is the sum of numbers 3, 6, 9.
So number 337 is quite coincident with 21 7 and 3, 6, 9! Three digits, many coincidences.

Two numbers which have not 321 number as number of digits (797 and 337) are also coincident with 21 7 and 3, 6, 9...
1. Both numbers have the same number of digits - 3.
2. Two three-digit numbers have together 6 digits.
3. Sum of these six digits is 36 (6*6, 6^2) and arithmetic mean of these digits is 6 - the same as arithmetic mean of the sequence 3, 6, 9.
4. Only one number appears only once in all six digits forming these two numbers together - that number is 9.
5. Arithmetic mean of sums of digits in these two numbers is 18 (3+6+9), it is ((23+13):2).
6. Only one of digits appears in both numbers 797 and 337 - that digit is 7.
7. Sum of digits which appears in both numbers together (two 7s from 797 and one 7 from 337) is 21, in addition, by concatenating numbers two (2) and one (1) we will receive 21; furthermore, sum of 7s in 797 is 14 and sum of 7s in 337 is 7, by concatenating 14 and 7 we will receive 147 (21*7).
8. Products of 7, 9, 7 and of 3, 3, 7 have the same sum of digits (9 - they are 441 and 63, respectively) and are divisible by 21; in addition, larger of these products is 7 times larger than smaller.
9. One third of all six digits in numbers 797 and 337 together is 3 (two 3s from six digits).
10. Sum of numbers 797 and 337 is 1134, which is a divisor of products of digits: 2, 1, 7, 3, 6, 9 (2268 - it is 1134*2) and a divisor of product of numbers: 21, 7, 3, 6, 9 (23814 - it is 1134*21).