Perhaps check it again

BMAD, I purposely did not include any solution like yours, because the OP in post # 1 and post # 5 stated that he/she wanted a subtraction sign used among the mathematical signs.

(9*(9 - 9))! = 1 ((9 - 9)/9)! = 1 I was looking for the square root symbol to do: (9 - sqrt(9*9))! = 1

((9 - 9)9)! = 1

"ONE HUNDRED AND TEN" is not standard. If that number, 110, were correct as a for instance, then it must be written as "one hundred ten." With this correction, this will naturally change the answer in the solution. Also, post # 12 is missing the count of the number of hyphens.

How is this supposed to be a valid puzzle? Is there some app on this site that allows users to measure lengths of sides of line segments? If there isn't a way to determine lengths of sides, then users can't confirm prime side lengths.

This problem isn't presented clearly. 1) The shortest track from A to B ON the sugar cubes might entail going through the tunnel and ON the sugar cubes. 2) "Through the shortest tunnel!?" There is only one tunnel. That is, there is only one hole. If you mean going from A to B *without* passing through the hole (and be the shortest route), then you're going to have to state that. And then if you mean the return trip from B to A must pass through the hole (and be the shortest route), then you are going to have to state that as well.

x7 + x6 + x5 + x4 + x3 + x2 + x + 1 (Please do it without using the assistance of a computer, calculator, or mathematics formula book.)

In post # 1 in the right-hand column under "a^2 - b^2," the next line should be "a^2 + b^2 + 2ab - 2ab - 2b^2."

BMAD posted: ---------------------------------------------------------------------------------------------------------------------------------- "How many dominoes are needed before the TOP [my emphasis] domino is one full horizontal length away from the edge of the table, for a full overhang length of 2?" ---------------------------------------------------------------------------------------------------------------------------------- The second diagram of post # 2, and the diagrams of post numbers 3 and 4 of DeGe do not count, and the diagram of TimeSpaceLightForce in post # 6 also does not count, because none of those scenarios involve the top domino being the domino that is doing the overhanging away from the edge of the table.

I resurrected this topic because it is missing a couple of key other solutions. The solution given so far is: (0! + 0! + 0! + 0!)! + 0! = 25 Here are two newer ones: ((0! + 0!)(0! + 0!))! + 0! = 25 ((0! + 0!)^(0! + 0!))! + 0! = 25 - - - - - - - - - - - - - - - - - - - - - - - - - Also, I am prepared to type other solutions in this thread that make use of the square root, floor, and ceiling functions to achieve the value of 25.

phil1882, what Prime offered does not count as I explained.

User Prime, your solution doesn't count, because it amounts the *same* solution repeated, that is, 0^2 + 1^2 + 1^2 = 2, that is, 0 + 1 + 1 = 2. Your 2nd and 3rd expressions don't give different sums of squares than your 1st expression.

The problem stated that they are "squares." "Squares" in the integer sense *means* unambiguously that the squares of integers are the only ones permitted, that is, 0, 1, 4, 9, 16, ...

@ BMAD, your solutions do not count, because sqrt(-25), sqrt(-100), sqrt(-9), etc. are not integers. A square (number) is the square of an integer and is necessarily nonnegative. @ Grimbal, it is not a question of whether someone accepts 0 as a square (number). It is a fact. Square numbers are the squares of integers. The phrase "in 3 unique ways" is ambiguous.