Show that 19*8^n + 17 isn’t a prime, where integer n ≥ 0
Slavy has a 7 day holiday. On any day, he’ll either rest (or recover), drink wine or drink beer. If he never changes drink type on consecutive days, in how many different ways can he enjoy his holiday?
e.g. he could drink wine for 7 days, but he cannot drink wine one day and beer the next.
(Any resemblance to a real person is entirely intentional).
If a single number, m, is removed from 1, 2, 3, …, n, the average value becomes 40.75.
Find m and n.
This is pretty easy, but requires some thought.
Completely solve n^2 + 20n + 11 = m^2 for integer m, n.
This is very easy if you use the right trick.
Well, maybe a little? The Trick of Mind solution will be to “Name a specific world’s country. A while back, I asked ToM an Easy and True solution about the Colebrook-White with six different equations. A Web site for the county’s computation asked me if they could publish the solution. I told YES, but for FREE. So they did a few weeks ago. Today they told me that about 1000 user have discovered my easy and true solution was right and they thanked me and the country’s web site. The web site told me today 883 folks from the country “love” it!
Some friends sat in a circle. Each had a whole number of dollars. The first had $1 more than the second, who had $1 more than the third, and so on. The first gave $1 to the second, who gave $2 to the third, and so on, each giving $1 more than s/he received, as long as possible. There were then 2 neighbours, one of whom had 4 times as much as the other. How many friends were there and how much had the poorest friend at first?
A bag contains either a white ball or a black ball, and each case is equally likely. A white ball is added. You now randomly take a ball from the bag. If it is white, what is the probability that the remaining ball is white?
I’m not sure if this has been posted before.
What are the last N digits of 9^(9^(9^9))? That’s a power tower of nines.
Make N as large as you can. Personally, I’m not going to aim beyond N = 8 as far too much work would be involved.
I’ve discussed the maths you need in my last post. You will need to use a 9+ digit calculator. The Windows calculator will do very nicely once you’ve worked out how to proceed.
Prove that p^6 – 1 is divisible by 504 for all primes p > 7.
Remember how to do the formula, X=10+Log(X)?
The easy answer, was to guess a value of X and figure the Log of it, and add 10.
That answer gives the next X which is much closer to the right X.
Repeat figuring the X until it does not change. It is the LOG function that makes the X increase buy a few decimals for each loop,
Wizard of Oz gave a very good answer of X = 11.04309064.
The next step has a little more variables but not much harder.
But done similar will give a good answer.
And Rr=0.023 and Re = 50,000
History says this can not be solved.
But for engineering design, 10 decimals is a great solution.
Once you find X then solve for “f” where f = 1/X/X
So find f with at least 10 decimals.
(I just figured f to 30 decimals)