4 and 5
very very tough math puzzle 2

The answer is this:
because the sum of the difference between all the adjacent numbers is 0. at the second three, we have a current sum of -3. So -3 + a + b + c + 4 - 2 = 0, where a b and c are equations:
i. 4 - x = a
ii. x - y = b
iii. y - 3 = c
Where iv. a + b + c = 1.
I'll let you guys do the simplification and substitution.
The answer is (clockwise) 4 and 4.5. Or 6 and 9, or ANY combination of numbers that gives a difference of 1 between the numbers 3 and 4.

In any circular list of numbers, the sum of the difference between all adjacent numbers is always zero regardless of what the numbers are. This is because (a-b) + (b-c) + (c-d) + ....(z-a) always cancels out everything to result in zero. So this really can't be the means of finding the solution. That being said, I really have no idea what the solution is supposed to be. Since there are ten numbers, it could be something like the length of words in counting to ten in some language or another, but not in any languages I know.

if you dont like the puzzles then dont waste your time trying to solve them. personally i take great interest in them and if a professional chess tutor says they are an essential part of learning and understanding chess then i will continue to try to learn from them.
Solve them if you enjoy them...but they have nothing to do with learning chess. To say they are "an essential part" of it is ridiculous.

if you dont like the puzzles then dont waste your time trying to solve them. personally i take great interest in them and if a professional chess tutor says they are an essential part of learning and understanding chess then i will continue to try to learn from them.
Solve them if you enjoy them...but they have nothing to do with learning chess. To say they are "an essential part" of it is ridiculous.
Problem solving, critical thinking, creativity, logic, pattern recognition. All are required when solving puzzles and problems.
Coincidentally, these are also extremely important if one is serious about climbing up the rating ladder in chess. Developing these basic cognitive skills would certainly help one's ability to IMPROVE at chess.

I don't think that's "certain" at all. It seems rather specious and fuzzy-headed to me.
And inasmuch as I've done a reasonable amount of improving at chess in my day, I imagine that I am as entitled to discuss these matters as you are (even though I can't quite seem to bring an equivalent amount of certitude to bear on the subject).

even though I can't quite seem to bring an equivalent amount of certitude to bear on the subject
That'll be your age.

lol...yeah. As a contemporary of Napoleon's once said of him: "I wish I could be as certain about anything as he is about everything."
We all start out as young turks and end up as old turkeys.

my first post got lost, let me try again....
when you look at the puzzle as a 3D image, by focusing into a distance, then something weird happen, you see 5 exact shapes, with numbers in them, they overlap:) perhaps I'm getting there right, friend???

What numbers should replace the question marks?
if you like this kind of puzzles join us in "Online Chess School"
"Online Chess School" is group for players who their rate under 1700 and want to improve their ability by using a systematic method not a random practice, it's like a real chess school , there are chess course will be processed in a long term and there are chess puzzles and IQ puzzles.
the aim of this group is to help those who love chess and want to ameliorate but they can't pay for chess lessons, on the other hand, the aim is to have a small friendly international community know each other very well and be friends forever.
Now we have just finished Lesson one , join us it's FREE
if your rate over 1700 and you like puzzles you are also welcomed
No chess games , No vote chess just chess lessons and puzzles
(HE SHOULDVE PUT IT IN OFF TOPIC)

my first post got lost, let me try again....
when you look at the puzzle as a 3D image, by focusing into a distance, then something weird happen, you see 5 exact shapes, with numbers in them, they overlap:) perhaps I'm getting there right, friend???
i tried this... i saw a uterus.... it had no numbers in it.

my first post got lost, let me try again....
when you look at the puzzle as a 3D image, by focusing into a distance, then something weird happen, you see 5 exact shapes, with numbers in them, they overlap:) perhaps I'm getting there right, friend???
i tried this... i saw a uterus.... it had no numbers in it.
did you switch the light on??
i said 6 & 9