MHBWhat is the Correct Value of r if 9!/(9-r)! = 840?
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The equation 9!/(9 - r)! = 840 was analyzed to find the correct value of r. Initially, r was thought to be 4, but upon recalculating, it was determined that 9!/(5!) equals 3024, not 840. Consequently, there is no integer solution for r within the range of 0 to 9 that satisfies the equation. The discussion highlights the importance of careful calculation in solving factorial equations. Ultimately, the conclusion is that the equation has no valid solution.
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
A power has two parts. Base and Exponent.
A number 423 in base 10 can be written in other bases as well:
1. 4* 10^2 + 2*10^1 + 3*10^0 = 423
2. 1*7^3 + 1*7^2 + 4*7^1 + 3*7^0 = 1143
3. 7*60^1 + 3*60^0 = 73
All three expressions are equal in quantity. But I have written the multiplier of powers to form numbers in different bases. Is this what place value system is in essence ?
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.