Math Puzzles 😊

As @J_SEDA_conant told me, and asked me to post the right answer to his puzzle is never. The ball comes back to the canon and does not hit the another ground.

@magicsacrifblunder I accidentally got that question right on #21 when I was trying to make sure if the problem was worded correctly.

@A_0123456 yes. Thats true. I asked myself the same, and because of that i asked in the forum if the question was trick. I didnt want to spoil anything.

#10, 38 -- Lol, @Thalassokrator , are you sure you're not a mathematician? Even if you're not, you still have a mathematician's mind. That's great that you investigate questions that intrigue you!

@BigBlunderGuy , your mathematical thinking is quite strong for a seventh-grader! Keep pursuing the things that interest you.

#34, 36 -- @dOnYa1386 , yes, in the U.S. there is some flexibility in the coursework. In larger schools the students generally have a greater variety of classes from which to choose. Also, we have what are called magnet schools which offer specialized programs such as math and science, technical or vocational (for a specific career) education, and fine or performing arts. Usually students need to submit an application or take an exam to get into these schools. Students attending a smaller school or living in a rural area generally have fewer choices. Maybe in your case, you can find an after-school class or a private teacher who might offer lessons in music?

#41 -- @magicsacrifblunder , @J_SEDA_conant , I should have been more suspicious of J_SEDA's post!

@rachel8
Yeah, I'm sure I'm not a mathematician, haha.
It took me an hour just to understand, that I was simply looking at a geometric mean. I rarely use them.
You're right in that I like to generalise things, to push myself and other's to the edge of my current understanding in order to learn something new. But I'm not smart enough to be anything more than (maybe) a hobby-mathematician.

And I agree, @BigBlunderGuy , you're really impressive! I was still trying to understand fractions in seventh grade! I certainly couldn't have come up with this conjecture of yours (though I now agree, that it seems quite obviously true, if one knows about arithmetic and geometric means).

Yes, there are always private teachers, but I think it would be better if these programs were available in schools.

x+x+1+x+2+x+3=840
=>4×+6=840
=>x= 834
So this is wrong.

1/12

4x+6=840
4x=834
x=208.5

@Ayushman_C @Ser_Raschupkin-01

It is not that x+x+1+x+2+x+3 = 840, (x)*(x+1)*(x+2)*(x+3) = 840. Also, you are solving for the highest number in the sequence, and not the lowest number.