I tried to visit the site but the page couldnt be loaded. My internet works fine. Is anyone else experiencing the same thing?

Hello all,

I ask as I was considering getting a copy and wanted to know what you thought of it and whether you’d be willing to post any pictures of the layout etc.

I can’t find any pages of it online, only a contents page and that’s about it.

Thanks

I've been playing with ternary strings.

Given any ternary string, construct a triangle, like an upside down Pascal's triangle, in which:

- The first row consists of the digits of the original string.
- Where adjacent digits in the same row are different, the digit below them is the third (unrepresented) digit.
- Where adjacent digits in the same row are the same, the digit below them is the same digit.

For example, the string 001022 generates the triangle:

0 0 1 0 2 2
0 2 2 1 2
1 2 0 0
0 1 0
2 2
2

Questions:

Consider the string formed from the digits down the left hand side of the triangle. When is this string the same as the original string (as in the example above)?

If we define a function that returns the latter string given the former string, then strings with this property are those with a period one cycle under iteration of this function. What patterns are exhibited by other strings under iteration? What variations on this function can be explored?

How does the number of ternary strings with this property vary with the number of digits in the string? (Remember these are strings, not integers, so leading zeroes count.) My sense is that this should be answered up to equivalence, where two strings are equivalent if one can be transformed into the other by, for example, replacing all 1s with 2s and all 2s with 1s. Up to equivalence, the number of ternary strings with this property of length n is (1, 1, 2, 2, 5, 5, 14, 15, ...) if I didn't make any mistakes. The deltas are thus (0, 1, 0, 3, 0, 9, 1, ...).

For interest, the fifteen eight-digit strings with this property are: 00000000, 00000011, 00001202, 00001210, 00001221, 00100100, 00100111, 00100122, 00101002, 00101010, 00101021, 00102201, 00102210, 00102212, 00102220.

[Edit to use code block for the example triangle so that leading spaces will show up. Oh wait, that didn't work. Oh well, I tried. And my second attempt at a fix didn't work either.]

I'm having trouble with this question.

The area of the SHADED AREA of the figure below is 81x^4 - 15xy -61y^2. What are the dimensions of the larger rectangle.

This is on the figure but not said on the question, it's a rectangle with top longer side being 3x and the length of it being 5y. If anyone can help with this question I'd be really happy since I have an exam tomorrow on quadratic and this questions been troubling me.

So there are 60 possible balls that could be drawn out, you will draw out 20 balls from the 60.

What are the odds of getting 4 particular numbers out of the 20 that are drawn out , and what are the odds of getting 3 particular numbers?

TL;DR: Should I not pursue math because of a low IQ and lack-lustre performance in Olympiads?

Context: I am a high-school student from India (11th grade). I have been active in Math Olympiad circles in my country for ≈3 years. I've achieved what I surmise to be the equivalent of (or a bit worse than) qualifying for the USAMO in the US. I am not bad at math, but I am far from exceptional. I've never had my IQ professionally tested, but online tests have consistently shown it to be somewhere in the low 120s. I will probably not pursue math as my major (which will probably be engineering) at the undergraduate level due to the educational circumstances in India and personal reasons, but I have been hoping to study it at a graduate level following my bachelor's. I definitely like and enjoy math, and I really want to love it, but I'm not sure if I do.

My question: Given that I have devoted a good amount of time towards Olympiad activities, but haven't achieved any significant success, and considering my relatively low tested IQ, should I aspire to a career in professional mathematics?

My problems with people saying IQ doesn't matter:

1. I've seen people — especially professional mathematicians — say that IQ doesn't matter and passion and hardwork go a longer way. I don't dispute this, but cannot help but notice that many of the people who say stuff like this are either obviously naturally gifted or unwilling to state their own IQ as a concrete counterexample.

2. "Math Olympiads are not reflective of professional research." Once again, I agree with the basic premise, but I do wonder how indicative they are of mathematical aptitude. It's undeniably true that a lot of people who have achieved success in professional math are also Olympians (e.g. Terence Tao, Timothy Gowers, Maryam Mirzakhani).

And I want to know whether the fact that someone like me, who has put in concentrated efforts (albeit less than some others), yet is largely unsuccessful at Olympiads, should continue to pursue math non-recreationally or just give up on that dream.

My apologies if this post is too long, off-kilter for this subreddit or kind of hackneyed. I wasn't sure where else to go.

Hi everybody! So I am preparing to add a percentage of increase in my resume and the numbers I got were reallllyyyyy high. Greatly appreciate it if you guys can look it over and confirm - TIA!!

feeling mighty embarrassed to post this >__< but better be dumb once and ask then to be a dummy forever

The customer base went from 130 to 240 within the time frame I was working - % increase I got was ~84% (pls see calculation below)

Percent Increase= (240−130​) / 130 × 100= ≈84.62%

The profit went from 35k to 95k, the % increase I got was ~171% - this is the # I am most concerned about, calculations below

Percent Increase=(95-35)/35×100= ≈171.43%

Im kinda hoping my calculations are off.....I don't know if my interviewers will believe these #s as they are pretty high...

eta - i have profit reports to back these #s

The Sunday NYT Book Review usually has a 1 or 2-page ad for self-published books. In today's edition, the ad includes a book entitled "Circle's True Pi Value Equals the Square Root of Ten." The blurb states that the author "reputes [sic] the old traditional approximation of Pi."

I really do not wish to spend the money to buy the book but am somewhat curious as to what his argument could possibly be. (Besides, isn't the real answer the sum of the square root of 2 and the square root of 3?)

Hello there, I am currently in grade 10, India. In my NCERT Textbook, it is given that in a system of two linear equations in two variable, say a1x+b1y=-c1 and a2x+b2y=-c2, if a1/a2 is not equal to b1/b2, there is only a unique solution whereas if a1/a2=b1/b2 but not equal to c1/c2, there is no solution for the given system of the two equations. Can anyone prove it as the proof is not given in my textbook? My mathematics teacher is subpar at best. I would like to clarify that I am not familiar with Matrices or Cramer's rule or some high level trigonometry. I would like the proof explained in such terms so that an avg. highschooler(aka me) can understand. Thank you

So that in the end, I can say A% + B% + C% + D% + E% + F% + G% = 100%

Example: (1+1+3+5) * 2 * 4 * 10 = 800

Definitions: A-D > Scalars, E-G > Multipliers, and A-G >Modifiers

For Scalars A-D:

What I tried:

• A = 1/800 = 0.13%
• B = 1/800 = 0.13%
• C= 3/800 = 0.38%
• D = 5/800 = 0.63%

Sum of above = 1.25% (if above values were not rounded)

Sum of Scalars = 1+1+3+5 = 10

Total percentage of Scalars = 10/800 = 1.25%

For Multipliers E-G:

Total percentage of Multipliers = (Total modifiers - Sum of Scalars) / total modifiers

(800 - 10) / 800 = 98.75%

multiplierE * x + multiplierF * x+ multiplierG * x = 98.75

2x + 4x + 10x = 98.75, > x= 6.17

Plugged back in:

• E = 2x = 2(6.17) = 12.34%
• F= 4x = 4(6.17) = 24.69%
• G = 10x = 10(6.17) = 61.72%

Sum of Multipliers = 98.75%

Which is: 790/800 = 98.75%

So:

A% + B% + C% + D% + E% + F% + G% = 100%

0.13% + 0.13% + 0.38% + 0.63% + 12.34% + 24.69% + 61.72% = 100%

Main question: Does this logic make sense...

Scalars:

1. To get the total Percentage of the scalars, they are out of the total Modifiers.

Multipliers:

1. To get the total Percentage of the Multipliers, (Total modifiers - Sum of Scalars) / total modifiers, that is basically getting the remainder of the Total Percentage of the scalars.
2. Then I represent each Multiplier * x, to show that they multiply rather than just add and that equals the Total Percentage of the Multipliers. Then once x is solved, I plug them back in to get the percentage of each Multiplier.

How is the logic in this (not so much the math), do you feel there would be better alternatives to represent the percentage of each modifier compared to the total Modifiers or do you feel the logic behind this makes sense?

Let me know and if you feel there is a better alternative(s), please explain/show the logic, thank you!