One way of counting the number of ways of making change is first to define: F(k) = floor(k/2)+1 which for k=0,1,2,3,..., is 1,1,2,2,3,3,4,4,... and which is...
... and ... of ... = ... I agree. I meant finding a solution is easy. I don't know why this is the only solution. Of course, this is Sloane sequence A000008. I...
Gentlemen: I found this problem in a math site (Certamen el Numero de Oro 1998) and I have been unable to find its solution. Would some one of you, members of...
... k can take 3 forms: 3m,3m+1,3m+2. (3m)^3 + 1 = 27m^3 + 1. This is not div by 3. (3m+1)^3 + 1 = 27m^3+27m^2+9m+1 + 1. This is not divisible by 3. ...
... 9. then ... impossible. ... Very clever and interesting. But what is special about 3? Could this type of proof be done with another number, say, 5? ...
... Well it is proved that if P(n) = the product of the first n primes then P(n)-1 can not be a cube for n > 1. The question to ask is can this type of proof...
... of ... proof. ... 2,3,4 ... expansion ... coeficient C ... Two observations: (a)When you extend the argument to proof that p(n)-1 can not be a 5th, 7th,...
... by ... Not exactly. However, the concept of divisibility can be generalized. Using the "forms" notation (which I prefer to the modulo) a number k is of the...
... But the proof depends upon P(n) being divisible by the 1st power of the nth prime but not the square of the nth prime. P(k) is not divisible by the nth...
... 3. ... divisible ... is ... of ... proof. ... generalized. ... k ... coefficients ... The original question can be generalized. Your proof works when N + 1...
Here is a question someone posted on Yahoo Answers which I think never got fully resolved. Suppose we shuffle a standard deck of cards. What are the...
Can you help me to find out how to calculate (create a formula)the summary 1(1!)+2(2!)+3(3!)+4(4!)+...+n(n!)? Thanks (and if you can I would appreciate if you...
... question someone posted on Yahoo Answers which I think never ... rank ... total number of cards is ... the cards on the rank ... second card ... story. ......
... question someone posted on Yahoo Answers which I think never ... total number of cards is ... the cards on the rank ... second card ... Mohanad, I've tried...
... There are 293 ways to make change for a dollar, but only if you include a silver dollar among your coins. Here is a generatingfunctionological approach. ...
Studies show goldfish have memories of more than 3 seconds. The speaker of the house can speak. He can't take sides in a debate, he effectively chairs the...
For A + B + C = 360 degrees Prove that [sin(A) + sin(B) + sin(C)] is maximum when A = B = C I kind of see a pattern on excel in favor the proof but just...
Hello Positive and informative responses in my first question 6 years ago http://tech.groups.yahoo.com/group/mathforfun/messages/3391?threaded=1&m\ ...
Hello Positive and informative responses in my first question 6 years ago encouraged me to post my second puzzle in this forum that its membership with...
During a workout a runner starts on a flat surface and runs at 8 mph. She then goes up a hill at 6 mph. She turns around and retraces her route going 12 mph...
Since the distance uphill and downhill are equal, and they average 8 mph, it would be the same as running 2 hours at 6mph. Therefore the total distance is 12...
... wondering if ... Except for a factor (1/2) this is the area of the triangle formed by three points on a unit circle where A,B,C are the arc angles between ...
Having problems with message search?
Fill out this form to ensure your group is one of the first to be migrated to the new message search system.
