


Topic, Math Whiz Quiz Game V2  
 
You must register or log in to post a message.@Simon: your explanation is much faster and less complicated than mine. Just a small precision: at the (n2)th point, you still have 2 possibilities (2 points remaining). The result (n1)! has to be divided by 2 because each polygon is counted twice (for example ABCDE is equal to AEDCB). Edit: I think I scrambled the n = 4 and n = 5. So I'm also guessing it's (n1)!/2, but I don't have a conclusive proof. My explanation for (n1)!/2 is: start at a random point, now you've n1 options to draw a line to another point, at this point you've n2 options, etc untill at the n2th point you don't have any options anymore, so it becomes (n1)!/2!=(n2)!/2 Let A, B, C, D the four points. One polygon is ABCD, identical to BCDA, CDAB, DABC, DCBA, and others obtained by circular permutation and by putting the points in the reverse order. Then, the 3 different polygons are ABCD, ACBD and ACDB. Do you agree? edit: I think that the solution could be (n1)!/2  for n=3, there is one solution ABC  for n=4, we obtain the new polygon by inserting the point D in each of the vertices of ABC: ADBC, ABDC, ABCD (3 solutions)  for n=5, we do the same for each of the 3 previous polygon. for example, ADBC gives AEDBC, ADEBC, ADBEC, ADBCE (4 solutions multiplied by 3 = 12 polygons).  for n, the number of polygons should be 3*4*5...(n1) = (n1)!/2 Suppose you've n points in the plane, where no 3 points are colinear. How many different polygons(ngons) exist with the n points.(you have to use all points). I found 4 polygons for n = 4. (72+46+7+3+3+1+1):7=19 ( all points in total : amount of players = average points ) = 2(x^3/e^2x) = 2(3x^2*e^2xx^3*2e^2x)/(e^2x)^2 = 2(3x^22x^3)/e^2x = 2x^2(32x)/e^2x circle: (x2)^2+(y3)^2 = 25 subsituting x2=y > (y)^2+(y3)^2=25 y^2+y^26y+9=25 2y^26y16=0 D=364*2*(16)= 164 y=[6 +/ sqrt(164)]/4 y = 3/2 +/ sqrt(41)/2 Intersection points found with x = 2y [x = (1+sqrt(41))/2, y = (3sqrt(41))/2] = [x = 3.70, y = 1.70] and [x = (1sqrt(41))/2, y = (3+sqrt(41))/2] = [x = 2.70, y = 4.70] 3x = y and 6x+y = 54 6x = 2y ==> 2y+y = 3y = 54 ==> y = 18 3x = y ==> x = 6 2y+x = 2*18+6 = 42kr 5A+6B=80 10B+6B=80 16B=80 B=5 ==> A=10 Conclusion: He bought 10 apples and 5 bananas. V = (pi/3)*8cm*((2.3cm)^2+2.3cm*3.3cm +(3.3cm)^2)= 199.135 cm^3 Dice problem(2p) Chance to have 2 dices with same number up is (1/6)*1/6)=1/36. We have 6 sides so chance is 6*(1/36)=1/6. And now I forgot to check how many point Simon was going to get. Was it four? 2) coordinates of centre of circle "x^2+y^2=25" is (0,0) and radius 5.  GeneralFirst post of the topic I post maths questions, and then it's up to you guys to find the answer(s), preferably with some kind of explanation.  The first to post the correct answer, gets the points.  The number of points any question gives, is stated along with the question itself. Few points → Easy question, and oposite.  New questions will be added whenever the previous one(s) have been answered correctly. CURRENT QUESTION(S): What is the average score of Math Whiz Quiz Game V2? (1p) LEADERBOARD: Nelson90: 72p SimonM: 46p Jim674: 7p Gameinsky: 3p PineappleDude: 3p Demonicyoshi: 1p Psychomaster: 1p Treazer: 1p Signs explanation 