Squares and Median
The sum of 3 different positive integers is 55. The sum of any two of them is a perfect square. What is the median of these three positive integers?
Posts
Making Perfect Squares
The sum n2 + 2020 is a perfect square. What's the sum of all positive values of n?
Counting Perfect Squares
The perfect squares are the squares of the integers. How many perfect squares are there between 20 and 2020?
Counting Squares
48 CMM students have a meetup together. Each holds a square tile. They lay the tiles down to form a big 7 by 7 grid, with the center position empty. How many squares are there that are fully covered by tiles.
Perfect Squares
The whole numbers 8, 10, 15, 17, 21, and 28 are arranged, without repetition, in a horizontal row so that the sum of any two numbers in adjacent positions is a perfect square. Find the sum of the middle two numbers.
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A similar problem was given in Assignment 1 of Charlotte Math Meetup.
The whole numbers 3, 4, 5, 6, 12 and 13 are arranged, without repetition, in a horizontal row so that the sum of any two numbers in adjoining positions is a perfect square. Find the sum of the middle two numbers.
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A similar problem was given in Assignment 1 of Charlotte Math Meetup.
The whole numbers 3, 4, 5, 6, 12 and 13 are arranged, without repetition, in a horizontal row so that the sum of any two numbers in adjoining positions is a perfect square. Find the sum of the middle two numbers.
Squares in Fractions
Calculate:
-(1^{2}+3^{2}+...+97^{2}&space;+99^{2})}{1+2+...+99+100} "\frac{(2^{2}+4^{2}+...+98^{2}+100^{2})-(1^{2}+3^{2}+...+97^{2} +99^{2})}{1+2+...+99+100}")
.
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A similar problem was given in Assignment 3 (Level M) of Charlotte Math Meetup:
Calculate:
-(1^{2}+3^{2}+...+97^{2}&space;+99^{2})}{1+2+3+...8+9+10+9+8+...+3+2+1} "\frac{(2^{2}+4^{2}+...+98^{2}+100^{2})-(1^{2}+3^{2}+...+97^{2} +99^{2})}{1+2+3+...8+9+10+9+8+...+3+2+1}")
.
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A similar problem was given in Assignment 3 (Level M) of Charlotte Math Meetup:
Calculate: