Don't confuse intellect and chess skill. It's one of the biggest tropes I'm super sick of. Sure, being smart doesn't hurt your chess ability, but it doesn't make it either. Chess is a game and it really has very little to do with pure, abstract intelligence.
To answer the prime number question, it's 0, because 2 * 5 puts a factor of 10 in there and then it doesn't matter how many other numbers you multiply it by, it's always going to end in a 0
Back in middle school when I was doing math competitions (namely mathcounts) there was a question asking what the last two digits of the product of all the primes up to 100 (or maybe it didn't include 5 or something) so the only way to do it was to list all the primes and do math.
I got that answer as well, except I thought he said "All the numbers up to 1,000,000", not "all primes". Same logic though. Not sure I would've thought of it if I'd heard the question correctly.
Chat should have asked a chess-related problem just to be extra annoying. Here is one: Two queens are randomly placed on distinct squares of a chessboard. Determine the probability that they attack each other. Try generalizing to an n by n board for positive integers n>1 for an extra challenge, or maybe try different pieces.
Eric, that was an amazing display! The way you battled from behind the whole game and behind in time, showed vulnerability, knew your opponent’s rating and everything else made quite the video lesson! I marvel at your ability. Great to see and keep making us St. Louis peeps proud!
A look into the life of the bishop living on Diagon Alley, cobbled by dark stones. Never crossing paths with those who tread on the light coloured streets
The math question about the last digit if you multiply all the prime numbers below a million turns out to be an easy question to answer. The first and third primes are 2 and 5, and when you multiply them, you get 10. Any multiple of 10 ends in a 0.
@@Bravo-oo9vd I can certainly understand how Rosen needed so much focus on that game that he couldn't bother working that out. I suspect that if he weren't in the middle of a tough game, he would have come up with the answer. He seems to be a pretty smart guy.
This is actually one of the few two knights variations I’ve really studied, and fxg3 instead of hxg3 is a slight improvement. You’ll see that after cxd4 O-O white scores pretty well.
11:10 for the case of 1 digit number 'a': a = 3a a = 0 0 isn't positive, so is outside the scope of the claim for the case of 2 digit number 'ba': a+10b = 3(a+b) 7b = 2a 2&7 are the only digits with this ratio, so ba can only be 27 for the case of 3 digit number 'cba': a+10b+100c = 3(a+b+c) 7b+97c = 2a c must be at least 1 for cba to be a 3 digit number instead of 2 digit, making the left hand side too big for the right hand side to equate, even with a=9 for the case of more than 3 digits, the left hand side just grows bigger and bigger while the right hand side remains as 2a, meaning the only positive integer that satisfies this condition/equation of any digit length was 27
at 12:32 the answer should be 0 right? because every prime number which is less than 1 million is odd except for 2 and we know that the multiplication of the digit 5 with other odd numbers gives 5 as the last digit and finally when we multiply it by 2 we have 5*2=0.
The number 27 fact is true because if we assume that there is for example a triple digit number abc that's 3 times the sum of its digits then we would get 100a + 10b + c = 3a + 3b +3c That is 2c = 97a + 7b Now a, b and c are all supposed to be single digit numbers and obviously none of the single digit numbers are 97 times something + more It just becomes worse with more than 3 digits Edit: Oh and there can't be other double digit numbers because you would get like 7a = 2b which is only possible if a is 2 and b is 7 because 7a = 2b implies that 2b is divisible by 7 and so b being a single digit number must be 7
Except that you are assuming "a" is not 0 for the last step of your reasoning here. So you are really only showing it doesn't work for triple digits. But that doesn't make 27 the only solution. It just means you need to have a = 0, and then 2c = 7b. So 27 is a solution to that, but there is also 0.
Caleb Denby has a very detailed video about this line in the Two Knights Caro Kann on the St. Louis Chess Club UA-cam page. I recommend it for anyone interested.
Eric won vs prince if Yemen. If its true prince of yemen you should better let him win. Devil numbers everywhere. Finish after 66 moves. What if he get rage and let you assasined?😮
27 is actually the only positive integer that's 3 times the sum of its digits. Lets say that we are searching for such a number with digits a0, a1, a2, ..., an The equation we would like it to verify is: a0 * 1 + a1 * 10 + a2* 100 + ... + an * 10^n = 3 * (a1 + a2 + ... + an) or -2 * a0 + a1 * 7 + a2 * 97 + ... + 999...997 * an = 0 The a2, ..., an digits can only be zero, or else the left part would be strictly positive and the equation wouldn't hold, so we are left only with the first two digits satistfying the equation: -2 * a0 + a1 * 7 = 0 or a0 * 2 = a1 * 7 Notice that the left part of the equation is a multiple of 2 and the right one is a multiple of 7. So we are searching for common multiples of 2 and 7. The smallest one is 14, which we can achieve with a0 = 7 and a1 = 2, that is the number 27. Also there are no solutions for higher common multiples, since the digits can only go up to 9. For example in order to have a0 * 2 = a1 * 7 = 28, we would need a0 = 14 which is not a decimal digit. So actually 27 is the only positive integer with this property.
I couldn't help but be amused that your "Oh no my knight" gambit to take queen was going exactly as planned, but then you spent 2½ minutes recalculating to change everything. Did I miss a big reason for that?
The "oh no my knight" was what they call "hope chess". He reasoned that his opponent was well prepared, and that it wouldn't work. So he calculated the line out 7 moves or so and found he was down a pawn, so he went for the rook lift strategy, which incidentally also didn't work.
Yes, he realized that his opponent could play Bc5 instead of Qxd4 right away and would be in trouble. The knight would effectively be pinned in a place that would be hard to defend against the Bishop and Queen battery. He didn't see Bc5 when he first saw the funny line but did after a few moves into the line and decided to leave the pawn there since it wasn't safe to take yet. He also didn't want to move his knight so that he could continue to protect e5 pawn and have the possibility to take d4 later.
Dude I hate it WHEN YOU CAN SEE someone is obviously in a match concentrating, trying to think and some guy feels the need for attention to donate $5 with lines upon lines of text. At least have the decency to wait until the match is over so nobody, not just Eric, gets distracted by the TTS voice yapping on. 4:43 This is sadly a very common occurence in many streams where these people are incapable of reading the room and then sometimes even get mad if "the streamer" doesn't react to that donation. God these selfish people make me mad.
Disrespecting open source developers is extremely silly. The fact that they can support a huge number of users running on donations alone without selling your data is awesome. If you want more features maybe you should learn programming and open a pull request.
And maybe you should learn to mind your own business. I wasn't opening this for debate. Everyone knows they do absolutely nothing to fix bugs. Nothing. There are issues going back a decade they haven't bothered to touch. They don't do very much of anything and everyone knows it. It's just fact. Who are you trying to impress? Save your white knight schtick for someone who cares.
Maybe you should learn to mind your own business. I wasn't opening this for debate. Everyone knows they do absolutely nothing to fix bugs. There are issues going back a decade they haven't bothered to touch. It's just plain fact and everyone knows it. Who are you even trying to impress with your white knight schtick? Save it for someone who gives a crap.
And maybe you should learn to mind your own business. I wasn't opening this for debate. Everyone knows they do absolutely nothing to fix bugs. Nothing. There are issues going back a decade they haven't bothered to touch. It's just plain fact and everyone knows it by now. Save the white knight bit for someone who cares.
Sometimes when I play chess I physically shake in disgust at my lack of intellect
Don't confuse intellect and chess skill. It's one of the biggest tropes I'm super sick of. Sure, being smart doesn't hurt your chess ability, but it doesn't make it either. Chess is a game and it really has very little to do with pure, abstract intelligence.
Don’t be! Chess like most skills is almost entirely practice and pattern recognition
It's like rubiks cubes in that way too^
Why you dont taka pawn on d4 and he cant win back bcs of bishop b5 check taking hid Queen????
26.47
To answer the prime number question, it's 0, because 2 * 5 puts a factor of 10 in there and then it doesn't matter how many other numbers you multiply it by, it's always going to end in a 0
Back in middle school when I was doing math competitions (namely mathcounts) there was a question asking what the last two digits of the product of all the primes up to 100 (or maybe it didn't include 5 or something) so the only way to do it was to list all the primes and do math.
I got that answer as well, except I thought he said "All the numbers up to 1,000,000", not "all primes".
Same logic though. Not sure I would've thought of it if I'd heard the question correctly.
Chat should have asked a chess-related problem just to be extra annoying. Here is one: Two queens are randomly placed on distinct squares of a chessboard. Determine the probability that they attack each other. Try generalizing to an n by n board for positive integers n>1 for an extra challenge, or maybe try different pieces.
You are right! I was just about to post the answer: 5, and then I saw your answer. I forgot that 2 is a prime (the only even prime).
11:50 Black doesn't take on f3 because he is in check.
I finally realized that at 27:20 😅
A Grandmaster could somehow make it happen though.
Grandmasters are allowed to check when they are in check. It's FIDE rules.
Grandmasters can have a little illegal move, as a treat
I love the comment about how the opponent probably isn't a GM based on that 😂❤
Eric, that was an amazing display! The way you battled from behind the whole game and behind in time, showed vulnerability, knew your opponent’s rating and everything else made quite the video lesson! I marvel at your ability. Great to see and keep making us St. Louis peeps proud!
Staring Into Sadness: My Life as a Bishop. Available now wherever fine books are sold.
As in... Reuben Fine?
A look into the life of the bishop living on Diagon Alley, cobbled by dark stones. Never crossing paths with those who tread on the light coloured streets
Bishop staring into sadness ❌
Bishop staring into connect four ✔️
"Maybe if I was Bobby Fischer I would take the pawn." The sense of humor here is on another level. So many little gems.
Can you explain for us simple folk?
He is referring to a famous Bobby Fischer game against Borris Spassky. Fischer grabbed a "free" h pawn and got his bishop trapped.
Chat constantly saying maths questions made me laugh 😂
That was definately very funny. Eric fighting for his life on the board, fans in chat, "can you do that also while juggling"?
not remotely funny. Terribly disrespectful. I hate people who ask questions during tense games. Actually hate them.
I watched through to the analysis only to see if he ever realized he took the bishop with check. Glad he caught it
Chess is one of the only games that can get my heart pounding
You obviously don’t have a romantic interest.
@@joeb4142 I'm gonna assume that the original comment edited "things" to "games" after you replied, otherwise your comment is really out of place lol
@@rivetace You’ve never played sexual games with you s.o.? I feel sorry for you lol
you must have never been in top 5 during og fortnite
The math question about the last digit if you multiply all the prime numbers below a million turns out to be an easy question to answer. The first and third primes are 2 and 5, and when you multiply them, you get 10. Any multiple of 10 ends in a 0.
Thanks for the solution, I figured it must be even, because 2 is prime, but forgot about 5
@@Bravo-oo9vd I can certainly understand how Rosen needed so much focus on that game that he couldn't bother working that out. I suspect that if he weren't in the middle of a tough game, he would have come up with the answer. He seems to be a pretty smart guy.
Congrats on 667k subs
When the opponent wins connect four, and imrosen doesn't recognize it
underrated lmao
You're the best Eric! Thanks for all the awesome content. ❤
This is actually one of the few two knights variations I’ve really studied, and fxg3 instead of hxg3 is a slight improvement. You’ll see that after cxd4 O-O white scores pretty well.
Ya, I think one of the key reasons why fxg is better is to keep castling a good move. hxg makes castles kind of awkward either side.
Awesome game and great victory! Congrats Eric! I especially admire your endgame speed and accuracy.
12:33 0. this equation involves 2 and 5 which make 10 and no matter what you multiply it with it'll always end in 0.
11:10
for the case of 1 digit number 'a':
a = 3a
a = 0
0 isn't positive, so is outside the scope of the claim
for the case of 2 digit number 'ba':
a+10b = 3(a+b)
7b = 2a
2&7 are the only digits with this ratio, so ba can only be 27
for the case of 3 digit number 'cba':
a+10b+100c = 3(a+b+c)
7b+97c = 2a
c must be at least 1 for cba to be a 3 digit number instead of 2 digit, making the left hand side too big for the right hand side to equate, even with a=9
for the case of more than 3 digits, the left hand side just grows bigger and bigger while the right hand side remains as 2a, meaning the only positive integer that satisfies this condition/equation of any digit length was 27
That finish was fantastic! Great game Eric.
Ending was very intense, and very nicely premoved most of the moves
Those math facts were really taking a toll on eric
Still waiting for the Stafford at the Fujairah blitz tournament 👀
at 12:32 the answer should be 0 right?
because every prime number which is less than 1 million is odd except for 2 and we know that the multiplication of the digit 5 with other odd numbers gives 5 as the last digit and finally when we multiply it by 2 we have 5*2=0.
The number 27 fact is true because if we assume that there is for example a triple digit number abc that's 3 times the sum of its digits then we would get
100a + 10b + c = 3a + 3b +3c
That is 2c = 97a + 7b
Now a, b and c are all supposed to be single digit numbers and obviously none of the single digit numbers are 97 times something + more
It just becomes worse with more than 3 digits
Edit: Oh and there can't be other double digit numbers because you would get like 7a = 2b which is only possible if a is 2 and b is 7 because 7a = 2b implies that 2b is divisible by 7 and so b being a single digit number must be 7
Except that you are assuming "a" is not 0 for the last step of your reasoning here. So you are really only showing it doesn't work for triple digits. But that doesn't make 27 the only solution. It just means you need to have a = 0, and then 2c = 7b. So 27 is a solution to that, but there is also 0.
@@andeolevain The commenter stated that 27 was the only positive integer with the property, and 0 is not positive, so the statement is correct.
@@phoquenahol7245 My bad. I missed that. And actually, I wasn't even aware that zero wasn't positive in English.
5:55 my calculation was Nxd4 Bc5 c3 Nc6 Bb5, and white seems fine.
Opponent was probably like "what hit me" at game end.
5:35 can't you it still take it since the queen can't recapture because of the discovered check from the bishop. I guess Bc5
4:20 why not take the pawn with the knight and then pin the black knight with the bishop if it comes to c6?
Superb finish, Eric!
Absolutely insane finish, well done!
Turns out the way to troll chess masters as the audience is to pose them math questions
It felt like you had no breathing room in that opening. Nice job pulling a victory out of that! And of course... Go Pam!!
Black didn't take the knight on f3 because bishop takes d7 was a check
I‘m glad I’m not the only one who is shaking after games:-).
I did enjoy it. Thank you!
If we exclude numbers 1 and 2 and multiply the rest of the prime numbers up to one million, what is the the last digit of that number?
this game left me shitttingg
2:40 Nice Level 2 Arrow Geometry 👍🏻
Eric is in his evil phase
Funny how the game ended up being 66 moves after the discussion of sixes at the start haha
Caleb Denby has a very detailed video about this line in the Two Knights Caro Kann on the St. Louis Chess Club UA-cam page. I recommend it for anyone interested.
A regular game online.... been a while since we have had one of these.
At 8:39 does Bxd4 work?
2666 was the street address of Jules Stein's Chicago Chess Center 2666 N. Halsted St.
That was some clutchness. What a game 😳
Great finish!
What…a…game….
26:20 "Chat, you suck at chess and I would self destruct if I played the moves you suggest......no offense" - Eric Rosen 2024
Kappa
😆
That was excellent, very exciting ending
Zen Mode *sh'ts pants*
holy shit what a finish
I love you Eric!!!!
Wow what an exciting ending!
Oh no! I hope Eric didn't suffer any microaggressions in this video!
Does anyone have any of the answers of the maths questions, I’m low-key invested
11:09 duh! what about 72🙄
That was pretty boss
Great game. Cool shirt.
23:05 Never play f3
667 , now you can relax
Great win. Your time management is terrible, but you made it work there somehow.
Wow, amaznig game.
Eric gave me 500 rating points just for watching this video
26:13 savage 💀 not wrong, but savage.
Eric u are the best ❤
I saw your 666 earlier today😂 looks like you’re past it!
Eric you deserve 666 million subs
I don’t know if you noticed but your rating increased to 2666. You just can’t get away from the sixes.
Funny math distractions
Hmm. I'm 10min in, and the total time on the board says there's 11min left, but the video is 30min long. Oh boy
" It was a fun game " :)
Eric won vs prince if Yemen. If its true prince of yemen you should better let him win. Devil numbers everywhere. Finish after 66 moves. What if he get rage and let you assasined?😮
Eric's complaining about his subscriber number but then wins the game and makes his Lichess score the exact same number lol
day 2 asking Eric to say "bon appetit" in a video (I watch your videos when I´m having dinner)
Appropriate way to reach 2666 rating🎉😂
Lol my credit score is exactly 666 😭
I love Rosen. His chat is irritating.
27 is actually the only positive integer that's 3 times the sum of its digits.
Lets say that we are searching for such a number with digits a0, a1, a2, ..., an
The equation we would like it to verify is:
a0 * 1 + a1 * 10 + a2* 100 + ... + an * 10^n = 3 * (a1 + a2 + ... + an)
or
-2 * a0 + a1 * 7 + a2 * 97 + ... + 999...997 * an = 0
The a2, ..., an digits can only be zero, or else the left part would be strictly positive and the equation wouldn't hold, so we are left only with the first two digits satistfying the equation:
-2 * a0 + a1 * 7 = 0
or
a0 * 2 = a1 * 7
Notice that the left part of the equation is a multiple of 2 and the right one is a multiple of 7. So we are searching for common multiples of 2 and 7.
The smallest one is 14, which we can achieve with a0 = 7 and a1 = 2, that is the number 27.
Also there are no solutions for higher common multiples, since the digits can only go up to 9.
For example in order to have a0 * 2 = a1 * 7 = 28, we would need a0 = 14 which is not a decimal digit.
So actually 27 is the only positive integer with this property.
2666 Elo 😈😈😈
I couldn't help but be amused that your "Oh no my knight" gambit to take queen was going exactly as planned, but then you spent 2½ minutes recalculating to change everything. Did I miss a big reason for that?
The "oh no my knight" was what they call "hope chess". He reasoned that his opponent was well prepared, and that it wouldn't work. So he calculated the line out 7 moves or so and found he was down a pawn, so he went for the rook lift strategy, which incidentally also didn't work.
Yes, he realized that his opponent could play Bc5 instead of Qxd4 right away and would be in trouble. The knight would effectively be pinned in a place that would be hard to defend against the Bishop and Queen battery. He didn't see Bc5 when he first saw the funny line but did after a few moves into the line and decided to leave the pawn there since it wasn't safe to take yet. He also didn't want to move his knight so that he could continue to protect e5 pawn and have the possibility to take d4 later.
667.000 subs now ;)
I'm usually afraid I'll see a spoiler comment but there aren't any comments right now 😂
Dude I hate it WHEN YOU CAN SEE someone is obviously in a match concentrating, trying to think and some guy feels the need for attention to donate $5 with lines upon lines of text. At least have the decency to wait until the match is over so nobody, not just Eric, gets distracted by the TTS voice yapping on. 4:43
This is sadly a very common occurence in many streams where these people are incapable of reading the room and then sometimes even get mad if "the streamer" doesn't react to that donation. God these selfish people make me mad.
667k fiuf
You swallow so loud lmao
GG! Hahaha
Who cares cares about Hikaru! he meddles other peoples affairs!(botez , gm Eric Hansen)
sure seems like a stream sniper
Lichess developers... doing anything ever 🤣
Disrespecting open source developers is extremely silly. The fact that they can support a huge number of users running on donations alone without selling your data is awesome. If you want more features maybe you should learn programming and open a pull request.
And maybe you should learn to mind your own business. I wasn't opening this for debate. Everyone knows they do absolutely nothing to fix bugs. Nothing. There are issues going back a decade they haven't bothered to touch. They don't do very much of anything and everyone knows it. It's just fact. Who are you trying to impress? Save your white knight schtick for someone who cares.
Maybe you should learn to mind your own business. I wasn't opening this for debate. Everyone knows they do absolutely nothing to fix bugs. There are issues going back a decade they haven't bothered to touch. It's just plain fact and everyone knows it. Who are you even trying to impress with your white knight schtick? Save it for someone who gives a crap.
And maybe you should learn to mind your own business. I wasn't opening this for debate. Everyone knows they do absolutely nothing to fix bugs. Nothing. There are issues going back a decade they haven't bothered to touch. It's just plain fact and everyone knows it by now. Save the white knight bit for someone who cares.
Egghead....