BMAD

hmm well it does appear to be approaching 1/4 so maybe that is the limit.

I mean you said 5 but I said prove 6

Well stated but I have two issues: you said the max population is 6 but I asked you to prove for 6. Mutually unacquainted is not the opposite of mutually acquainted. I forget the English word for what I mean...is it contrapositive. As in ...if it isn't night it is day (mutual Acquaintances do not work this way)

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Are you sure? For some reason I am finding my area to be rounder in shape.

Oh. assume 50 50 chance

Prove that in any group of 6 people, at least 3 must be either mutually acquainted with each other, or mutually unacquainted with each other.

inspired by one of Bonanova's past problems: What proportion of the area of a regular n-gon is closer to its center than to any edge?

Ten out of 17 people suffer from plaque buildup, but Four out of five dentist agree that the new BMAD formula for mouth rinse will cure 95% of the people with gingivitis of plaque build up and is 85% effective for those who do not have gingivitis. If a random person is selected what is the probability they would be effectively treated of plaque buildup?

hmmm you may both be right. I was asked such a question and couldn't answer myself.

because?

Shamgar saved Israel by striking down 600 Philistines with an oxgoad. Assume the Philistine army were marching downhill in symmetry as follows: In The Leading Rows * one soldier in the first row * two soldiers in the second row * each row having one extra soldier until row n The Main Block * x rows of n + 1 soldiers The Trailing Rows * the leading rows in reverse: n soldiers in the first row, n - 1 in the next, down to a final row of 1 (the soldier whom Shamgar strikes directly with his goad) Thus, Shamgar struck the last man, who toppled the next row, who toppled the next row etc in a domino effect. What numbers of leading/trailing rows are possible? I'll give a couple of example possibilities: 1. zero: the main block would be 600 rows of 1 soldier 2. one: the main block would be 299 rows of 2 soldiers 3. two: the main block would be 198 rows of 3 soldiers

If you flip a coin n times and you get n-1 Tails from those flips, what is the probability that the coin is biased?

Well done! You answered my follow-up question nicely.

counting posts #7 & #8 together that is

besides we are assuming that all numbers are distinct

0,0 is not the only possibility for #1

Does there exist two squares such that their difference is a multiple of 4?

Remember if it is possible, to what extent is it possible, describe the total range of numbers

Consider the following definitions of perfect pairs/trios. If there exist such numbers that fit the definition show how many exist, if no number exists, provide a proof: (Each number is assumed to be distinct) 1. When you add two numbers you get a certain answer. Using the same two numbers, subtract the larger from the smaller and get the same answer in the first sentence. 2. Using three numbers, add the first two numbers together then divide the sum by the third number. The result will be one of the three numbers. 3. Two numbers whose sum is equal to their quotient.

no.

Make a 10 digit code using the digits 0-9 each once. Make another 10-digit code without any three adjacent code sequences repeating. How many unique codes can be made following these two rules? For example: code 1: 0,1,2,3,4,5,6,7,8,9 code 2 cannot contain 0,1,2 or 1,2,3 or 2,3,4 or ,3,4,5, etc. anywhere in its code.