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A country has three denominations of coins, worth 7, 10, and 53 units of value. What is the maximum number of units of currency which one cannot have if they are only carrying these three kinds of coins?
I know the formula for 2 denominations, but I don't know how to do one with 3.
Thanks, this doesn't exactly relate to bases, but:
Find all positive integers n such that
.The harmonic mean of two positive numbers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers (x, y) with x < y is the harmonic mean equal to 6^{20}?
Ok, so that 0.251 thing was correct. and the answer is 30 for the sum of the squares of the digit thing.
Given a rational number, write it as a fraction in lowest terms and calculate the product of the resulting numerator and denominator. For how many rational numbers between 0 and 1 will 20! be the resulting product?
We have fraction m/n. I wrote the prime factorization of 20!, but I can't seem to find the largest possible value of m. Once I get the largest value of m, then I can just count the number of divisiors of m, but what do I do to get m.
Also:
Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms.
Hmm 32/127 is what i found too
Also, anonimistefy, I got the 1st question. It was 30, not 32.
so apparently, we can have 2513 and stuff. So like we just need 251 in order and then can have extra digits. 251 /999 is interesting, because 251 is close to 250, a divisor of 1000, which is cllose to 999.
Anyways, idk about the 1st quesiton
EDIT: we don't need to have a repeated decimal
I thought that 999 was the answer at first. 800 yields 0.25125. Maybe there's something else in the problem I didn't comprehend. I'm going to get some clarification
The decimal representation of m/n, where m and n are relatively prime positive integers and m<n, contains the digits 2, 5, and 1 consecutively, and in that order. Find the smallest value of n for which this is possible.
yea, i got the 2nd question, but not the 1st.
The sum of two numbers (in base 3) will have a 2 digit?? Is that what you're saying?
also, 32 is not correct
Hi cooljackiec
I found that these numbers satisfy Q2.
I sort of see what you are doing here, but then again, I don't quite understand. We try to make sure that no numbers in our set are the arithemtic mean of two others. I've been suggested to use base 3, but I don't know how that would work.
EDIT: Turn our set into base 3 integers. Selecting those expressed with only 0 and 1 (base 3) gives us 2^k integers. I think this works, but I have to prove that this satisfies the condition of one number not being the AM of 2 others.
Do you have any ideas for the 2nd question?
Ok, we have N_b. Let's say N_b is in form of
. We wantWe just have to sum the squares of the digits in $N_b$. But finding the digits ain't viable. I don't have any ideas.
the sum of the squares of the base b digits are less than or equal to 512. I understand what N_b's value is, but i don't know about the values. Maybe trying smaller values of b would work.
Let b be an integer greater than 2, and let
(the sum contains all valid base b numbers up to 100_b). Compute the number of values of b for which the sum of the squares of the base b digits are less than or equal to 512. I understand what N_b's value is, but i don't know about the values. Maybe trying smaller values of b would work.[edited for clarity - bobbym]
Prove that from the set
one can choose 2^k numbers so that none of them can be represented as the arithmetic mean of some pair of distinct chosen numbers.halp. this equation
well for agnishom's first one, with the tangent to parabola, I got two values so naturally i took the smallest one. I somewhat get the ellipse solution
What is the maximum value of c such that the graph of the parabola
has at most one point of intersection with the line x+c?Consider the ellipse
Find the maximum value of the product xy on the ellipse.If (x - a)(x - 1) + 1 = (x + b)(x + c) is true for all x and if a, b, and c are integers, find the sum of all possible values of a.