Answer : 12 people. The 1st person can't shake hands with him/herself so has 11 handshakes, the 2nd person has 10 ....and so on. The total is 11 + 10 + ....+ 3 + 2 + 1 = 66. Another way is to use the formula to sum a range of consecutive integers from 1 to n. The Sum = ½n(n - 1) In this case, we can put, ½n(n - 1) = 66 then, 132 = n2 - n : n2 - n - 132 = 0 This equation can be factored, (n + 11)(n - 12) = 0 As we only require a positive integer solution, this is when n - 12 = 0, n = 12.
If there are n people, you have n*(n-1)/2 handshakes That gives the equation n*(n-1)/2 = 66 or n*(n-1) = 132 n2 - n - 132 = 0 (n - 12)*(n + 11) = 0 The solution to this quadratic are n = 12 or n = -11 Since the number of people cannot be negative, n must be 12.
66 inches is 66 inches.
66 inches is 66 inches.
Well, isn't that a happy little question! If you have 66 and you're looking to find out how many groups of 6 you can make, you simply divide 66 by 6. When you do that, you'll find that there are 11 groups of 6 in the number 66. Just imagine all those little groups happily fitting into 66, creating a beautiful mathematical landscape!
66 total handshakes are made. See related question at the bottom for the explanation.
66
If there are n people who shake hands with each other exactly once, it can be observed that there are n x (n-1) handshakes. Since each handshake is counted twice here,we divide this by 2. Therefore, total number of handshakes is n(n-1)/2. In the given problem, Given: Total handshakes =66 i.e n(n-1)/2=66 n2-n =132 n2-n-132=0 (n-12)(n+11)=0 n =12 or n= -11 As handshakes cannot be negative we discard 11 . Therefore answer is , 12 people.
66
Each handshake involved 2 people so 12 guests: Guest A made 11 handshakes, B 10 having already been counted as an A-B handshake, C 9 etc for 2 ppl thr is 1 hand shakefor 3 thr is 3(1+2)for 4 thr is 6(1+2+3)hence12 ppl coz..sum of 1st 11 is 66...
66-66+66= 66
66
Answer : 12 people. The 1st person can't shake hands with him/herself so has 11 handshakes, the 2nd person has 10 ....and so on. The total is 11 + 10 + ....+ 3 + 2 + 1 = 66. Another way is to use the formula to sum a range of consecutive integers from 1 to n. The Sum = ½n(n - 1) In this case, we can put, ½n(n - 1) = 66 then, 132 = n2 - n : n2 - n - 132 = 0 This equation can be factored, (n + 11)(n - 12) = 0 As we only require a positive integer solution, this is when n - 12 = 0, n = 12.
66 i think.
66 ones go into 66
66 33,2 11,3,2
If there are n people, you have n*(n-1)/2 handshakes That gives the equation n*(n-1)/2 = 66 or n*(n-1) = 132 n2 - n - 132 = 0 (n - 12)*(n + 11) = 0 The solution to this quadratic are n = 12 or n = -11 Since the number of people cannot be negative, n must be 12.