Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Suppose that one selects some subset of integers from the set {0,1,2,dots,44}. What is the smallest number to select to guarantee that two of the selected numbers sum to 44 ? Answer: 23

Suppose that one selects some subset of integers from the set {0,1,2,…,44} \{0,1,2, \ldots, 44\} . What is the smallest number to select to guarantee that two of the selected numbers sum to 4444 ?\newlineAnswer:\newline23 23

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 6right chevron icon
Powers with fractional basesright chevron icon

Full solution

Q. Suppose that one selects some subset of integers from the set {0,1,2,…,44} \{0,1,2, \ldots, 44\} . What is the smallest number to select to guarantee that two of the selected numbers sum to 4444 ?\newlineAnswer:\newline23 23
  1. Identify Pairs: We need to find the smallest number of integers to pick from the set {0,1,2,...,44}\{0,1,2,...,44\} so that at least two of them add up to 4444. Let's think about pairs that add up to 4444: (0,44)(0,44), (1,43)(1,43), (2,42)(2,42), ..., (22,22)(22,22). There are 2323 pairs here.
  2. Avoiding Pair Sums: If we pick one number from each pair, we can avoid having two numbers that sum to 4444. But as soon as we pick one more, we'll have to pick a number that completes a pair to 4444.
  3. Selecting 2323rd Number: So, if we have 2222 numbers, we might have (0,1,2,...,21)(0,1,2,...,21) or any other combination without a pair that sums to 4444. But when we pick the 23rd23^{rd} number, no matter what it is, it will create a pair that adds up to 4444.

More problems from Powers with fractional bases

Question
Write the expression using an exponent.\newline2×22 \times 2\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Evaluate the expression. 4−42 4 - 4^2 ____
Get tutor helpright-arrow

Posted 2 months ago

Question
x2=4x^2 = 4
Get tutor helpright-arrow

Posted 1 month ago

Question
x2=9x^2 = 9
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for x. \newlinex2=0x^2 = 0 \newlineWrite your answer in simplified, rationalized form. \newlinex=x = _____ or x=x = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for xx. \newline8=2x8 = 2^x \newline x=x = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for xx. \newline6=7x6 = 7^x \newline x=x = _____
Get tutor helpright-arrow

Posted 3 months ago

Question
Select the equivalent expression.\newline((8−5)/(2−2))−4=?((8^{-5})/(2^{-2}))^{-4}=?\newlineChoose 11 answer:\newline(A) \newline(820)/(28)(8^{20})/(2^{8})\newline(B) \newline(26)/(89)(2^{6})/(8^{9})\newline(C) \newline(1)/(8⋅22)(1)/(8\cdot 2^{2})
Get tutor helpright-arrow

Posted 4 days ago

Question
Select the equivalent expression.\newline(b745)−3= ?\left(\frac{b^{7}}{4^{5}}\right)^{-3}=\,?\newlineChoose 11 answer:\newline(A) b21415\frac{b^{21}}{4^{15}}\newline(B) 415b21\frac{4^{15}}{b^{21}}\newline(C) b−21⋅4−15b^{-21}\cdot 4^{-15}
Get tutor helpright-arrow

Posted 1 month ago

Question
Select the equivalent expression.\newline(33⋅66)−3=(3^{3}\cdot6^{6})^{-3}=?\newlineChoose 11 answer:\newline(A) 139⋅618\frac{1}{3^{9}\cdot6^{18}}\newline(B) 61839\frac{6^{18}}{3^{9}}\newline(C) 39618\frac{3^{9}}{6^{18}}
Get tutor helpright-arrow

Posted 1 month ago

View all (20)