bonanova
-
Posts
6975 -
Joined
-
Last visited
-
Days Won
66
Content Type
Profiles
Forums
Events
Gallery
Blogs
Everything posted by bonanova
-
Twenty friends, call them A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, decide to play bridge in foursomes for 5 days. To add to the fun, none of the players will have the same partner, nor play against any other player, more than once during the week. Can you provide the schedule of foursomes [NEWS] that will accomplish their wishes? Mon | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | Tue | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | Wed | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | Thu | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | Fri | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ | _ _ _ _ |
-
More than 200 years ago it was proved that any construction possible with a compass and straight-edge can be accomplished with a compass alone. It is a simple matter to find the midpoint of a line segment using a compass and a straight-edge. Find the midpoint of a line segment using a compass alone, without using a straight-edge. Or Google. To compare methods, consider that you are given the two points [0, 0] and [0, 1]. You are to locate the point [0, .5]. Bonus for the fewest steps.
-
Here are the totals, by word length, if you want to sort the results:
-
-
What a fascinating kind of problem! An easy problem for backtracking, but I know I haven't the time to debug a program... 5: Correct 6: Correct 7: Yes.
-
3: Yes. 4: Yes 2: - clever. but as you note, there is no solution for n=2.
-
4: Yes.
-
First string fails because there is not ONE digit between the pair of ONEs. Second string fails because there are not TWO digits between the pair of TWOs. I am going to amend the OP to eliminate the use of zeros. Thus, for the case of 1, 2, 3 we seek a string of six digits: 1 1 2 2 3 such that there are one digit between the pair of 1s two digits between the pair of 2s three digits between the pair of 3s. Again, forget the 0's.
-
-
Use the digits in pairs.
-
Not quite. There are three volumes to consider. The cylindrical hole The spherical end caps on either end of the hole cylinder The remaining volume of the sphere.It's the third item we seek.
-
Take a pair of zeros and place them together. 00 Note there are zero digits between the pair of zeros. Now place a pair of twos around them. 2002 Note there are two digits between the pair of twos, and still zero digits between the pair of zeros. It's straightforward to construct strings with this property using [only] the remaining even digits. 420024 64200246 8642002468 Let's include the odd digits, [Edit] and eliminate the zeros. For how many of these groups of digits, using the digits in pairs, can you construct strings with this property? 1 1,2 1,2,3 - clarify: for this case, arrange 1 1 2 2 3 3 to have one digit between the 1's, two digits between the 2's and three digits between the 3's 1,2,3,4 1,2,3,4,5 1,2,3,4,5,6 1,2,3,4,5,6,7 1,2,3,4,5,6,7,8 1,2,3,4,5,6,7,8,9 Have fun.
-
Hats on a death row!! One of my favorites puzzles!
bonanova replied to roolstar's question in New Logic/Math Puzzles
Question: Why not set up 219 combinations of tones of voice loudness speed pitch tap-dance steps language giggling clearing one's throat etc. that the first person uses in guessing his own color? The others can then immediately know their color. Answer: Because all of those things violate the terms of the OP, in which it is said no means of communication is allowed other than saying black or white.. -
Yes. Exactly. Elessar Adan has it also. I thought it was interesting....
-
Honorable mention on the Dozen part, gold star for over-achieving! Nice!
-
That was quick!
-
Take a common six-letter word and find at least a dozen 5-letter words by rearranging its letters. A bonanova gold star to the first to find a Baker's dozen. Your choice of six-letter words to start with. Enjoy!
-
-
It means greatest integer [whole number] that is not greater than {1/2 + square root[i]} Suppose i=2: 1/2 + sqrt[2] = .5 + 1.4142 = 1.9142. Floor {1.9142} = 1. In other words, round down to the next lowest integer.
-
Consider the integer sequence {a1, a2, a3, ..., ai, ....} where ai = i + Floor {.5 + i.5} And Floor {x} = greatest integer not greater than x What is special about this sequence?.
-
-
This is the sequence of square pyramidal numbers: an = {sum i=1,n} i2 Start with an nxn square array of spheres. place on them an [n-1]x[n-1] square array, and so forth up to a single sphere at the top. The entire square pyramid will have an spheres.
-
Correct. M and Z words exposed it nicely.
-
E: Yes. Puzzle solved.