## Search found 35 matches

- Wed Jan 31, 2018 7:46 pm UTC
- Forum: Logic Puzzles
- Topic: Longest Chess Word
- Replies:
**6** - Views:
**3918**

### Re: Longest Chess Word

Since pawns can provide up to 4 guaranteed moves in each file, to say nothing of all the other pieces that can legally move to that file, this is pretty much a referendum on the longest English word that doesn't use any of the letters I-Z. According to the CSW word list used for international Englis...

- Tue Jun 27, 2017 3:34 am UTC
- Forum: Logic Puzzles
- Topic: Crypto challenge
- Replies:
**5** - Views:
**5530**

### Re: Crypto challenge

If you have a full-size computer keyboard with numeric pad, look at the positions of the number 1-9 keys there as a grid. Within each string of numbers in the code, imagine drawing lines between the corresponding points in the grid, and the shapes you'll be drawing are just (a low-resolution attempt...

- Wed May 03, 2017 6:52 pm UTC
- Forum: Mathematics
- Topic: Halting Problem
- Replies:
**208** - Views:
**33572**

### Re: Halting Problem

No program, Oracle or otherwise, is entitled to special-case treatment that makes sure it's always the one with the ultimate right to react, in preference to anything else. In fact, the formal definition of the "programs" used in this context requires that if something exists as a program,...

- Mon Feb 27, 2017 10:57 am UTC
- Forum: Logic Puzzles
- Topic: A Fun Math Puzzle
- Replies:
**2** - Views:
**3604**

### Re: A Fun Math Puzzle

Huh? It's trivial to solve for the variables "dark gray square nested inside medium gray pentagon nested inside light gray hexagon emoji", "bunch of bananas emoji with at least four visible and possibly more concealed behind them", and "analog clock emoji showing 180 minutes...

- Mon Oct 31, 2016 2:39 am UTC
- Forum: Mathematics
- Topic: Finding a Quadrilateral for N Points
- Replies:
**20** - Views:
**4934**

### Re: Finding a Quadrilateral for N Points

No, it said nothing about the number of sides of any "concave areas" or "concave points", it defined S as the number of points which reside at vertices of the convex hull . Any collection of points will have exactly one convex hull, by the method which constructs a convex hull. I...

- Thu Oct 20, 2016 6:44 pm UTC
- Forum: Mathematics
- Topic: Finding a Quadrilateral for N Points
- Replies:
**20** - Views:
**4934**

### Re: Finding a Quadrilateral for N Points

Clearly each edge can contain a maximum of two points, so you can't do better than 8. Given any quadrilateral, it's trivial to pick two non-corner points from each edge to obtain a qualifying collection of 8 points that way, and given the eight vertices of a convex octagon, you can extend out altern...

- Wed Oct 12, 2016 4:21 pm UTC
- Forum: Mathematics
- Topic: Factorization using modular arithmetic
- Replies:
**41** - Views:
**9920**

### Re: Factorization using modular arithmetic

If you could find, without trials, an integer D that evenly divides N, then the problem of factoring N is solved even more directly, without having to slow the algorithm down with excess transformations to and from some other form! Is it possible? Sure, you just have to get really, really lucky ever...

- Tue Oct 11, 2016 8:42 pm UTC
- Forum: Mathematics
- Topic: Factorization using modular arithmetic
- Replies:
**41** - Views:
**9920**

### Re: Factorization using modular arithmetic

"Smartly choosing the starting value" is trivially sufficient for factoring any composite number even by trial division, since you just have to "smartly choose" one of the factors itself. The mere fact that it's possible doesn't lead to any constructive method for actually findin...

- Fri Jul 29, 2016 10:56 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**15629**

### Re: Theorem and consequences

The n=3 special case of Fermat was already proven by Euler, long before Wiles came along.

- Thu May 26, 2016 10:51 pm UTC
- Forum: Logic Puzzles
- Topic: Open puzzle about game
- Replies:
**36** - Views:
**6816**

### Re: Open puzzle about game

Figures for the delayed-cutting version: ⋅ 22 is now the smallest possible bid that allows you to craft a shape that cheese-blocks an opposing bid of 89 ⋅ 64 is the largest possible bid that allows you to craft a shape that is guaranteed to be cheese-proof ⋅ If both pla...

- Wed May 25, 2016 12:40 pm UTC
- Forum: Logic Puzzles
- Topic: Open puzzle about game
- Replies:
**36** - Views:
**6816**

### Re: Open puzzle about game

The smallest piece that can block a "swiss cheese 10x10" piece from coexisting on the board is 13 units, such as a 5x5 letter H, or three edges of a 5x5 square. The thing about swiss cheese battles, though, is that they lead to a kind of anti-speed creep, up to and beyond the precipice. Ob...

- Thu Mar 24, 2016 2:08 am UTC
- Forum: Mathematics
- Topic: Math without even numbers?
- Replies:
**40** - Views:
**9103**

### Re: Math without even numbers?

0 is an even number as well. What is 1-1 supposed to be, or is subtraction even going to be defined at all? (Without zero, you don't have an additive identity, so it seems silly to speak of an additive inverse.)

- Fri Mar 11, 2016 8:05 am UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**3460**

### Re: Three Water Tanks

That makes a simple quaternary search possible, in fact, and enables the space to be exhausted within 4 hours. Start by putting in requests for 150, 100, 50 -If 150 hit (so we are in [150,200]), then the other two necessarily also hit. 300 has been drained, and 150-300 may be left overall. Use the s...

- Fri Mar 11, 2016 4:35 am UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**3460**

### Re: Three Water Tanks

It can be done in 7 hours, plus a negligible amount extra that accounts for time to react to each printout as it arrives, and to move from one tank's control panel to the next. Note that the system is guaranteed to have enough water for at least the first three drainings that are less than or equal ...

- Thu Mar 10, 2016 6:37 am UTC
- Forum: Mathematics
- Topic: Goahead52's posts about primes
- Replies:
**17** - Views:
**3520**

### Re: Subsets and product of primes

First off, your term for 6 is wrong: the minimal partition there is actually 3,5,11 vs. 2,7,13 (165 x 182), for a sum of 347. With the correct value in its place, we find https://oeis.org/A182987 .

- Thu Mar 03, 2016 6:38 pm UTC
- Forum: Logic Puzzles
- Topic: Optimize tiling for a 50x50 grid
- Replies:
**7** - Views:
**3347**

### Re: Optimize tiling for a 50x50 grid

A 5x5 tile is worth 20, so filling the board with them scores 2000, not 1500. This makes the per-square efficiency 0.8, compared to the 1 point per square of the most efficient tile, the 4x4.

- Sat Feb 13, 2016 10:42 am UTC
- Forum: Logic Puzzles
- Topic: Unknown Digits
- Replies:
**6** - Views:
**2297**

### Re: Unknown Digits

Since apparently there's supposed to be some kind of logic (?) from which actual deductions can be drawn, it's rather easy to show that the letters can't have any kind of consistency to them across options, without appealing to a brute force printout. The two expressions that each represent T are &q...

- Tue Dec 29, 2015 3:27 am UTC
- Forum: Logic Puzzles
- Topic: Eight by eight matrix, flip a coin.
- Replies:
**3** - Views:
**2044**

### Re: Eight by eight matrix, flip a coin.

Randall sets the initial array of heads and tails and selects a coin, then based on that choice, you select any coin (not necessarily the same one) and flip it over, then the partner (who has not looked at the initial array of coins, and has not communicated with you since you were first able to see...

- Wed Dec 09, 2015 4:44 am UTC
- Forum: Mathematics
- Topic: The minimum wins access to playoffs in NBA
- Replies:
**4** - Views:
**1962**

### Re: The minimum wins access to playoffs in NBA

By rule, no game is supposed to end in a tie: if the game stays tied, you keep playing 5-minute overtime periods until the tie is broken after one of them, much like there's no hard limit on the number of extra innings a game can last in MLB. Logistically, the team has to be at their next scheduled ...

- Wed Dec 09, 2015 3:10 am UTC
- Forum: Mathematics
- Topic: The minimum wins access to playoffs in NBA
- Replies:
**4** - Views:
**1962**

### Re: The minimum wins access to playoffs in NBA

There are two conferences, each conference has 3 divisions, and each division has 5 teams. There are 8 playoff spots to be divided among the 15 teams in each conference, allocated such that the team with the best record in each division is guaranteed a spot, and the remaining 5 spots go to the teams...

- Fri Nov 13, 2015 3:26 am UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**50044**

### Re: Escape the Frictionless Circle

Stand on the gold brick. Wrap the cord around your waist repeatedly to get rid of the slack until it is taut, then lunge up and in some direction. If you can jump with enough force to nudge the brick up off the ground by any amount (let's say it outweighs the average person by 2:1 so you'd be liftin...

- Mon Nov 02, 2015 7:39 am UTC
- Forum: Logic Puzzles
- Topic: Squares and sequence
- Replies:
**5** - Views:
**2036**

### Re: Squares and sequence

1x8 + 2x7 + 3x4 + 5x6 already gets you 64, and 1x7 + 2x3 + 4x5 + 6x8 gets you 81.

- Thu Oct 08, 2015 9:02 am UTC
- Forum: Mathematics
- Topic: Set of particular numbers
- Replies:
**14** - Views:
**2649**

### Re: Set of particular numbers

Starting from n=2, the sequence eventually settles into a loop of 40 repeating numbers, which first stabilizes with the 20th term: 17653671, 1743552, 830081, 33554462, 53476, 873607, 18470986, 421845378, 34381644, 16824695, 404294403, 387421546, 17651084, 17650799, 776537847, 20121452, 3396, 3874671...

- Wed Oct 07, 2015 5:10 pm UTC
- Forum: Logic Puzzles
- Topic: Timed Bridge Problem
- Replies:
**5** - Views:
**3411**

### Re: Timed Bridge Problem

If Adam is responsible for holding the lantern the entire time, you get AD A AC A AB, for 2A + B + C + D. This could be faster, or it could not--the specific times aren't given, so we have no way of knowing whether 2B is faster or slower than A+C. We would need to know this in order to determin...

- Sat May 02, 2015 3:47 pm UTC
- Forum: Mathematics
- Topic: M.S:
- Replies:
**3** - Views:
**1723**

- Wed Feb 11, 2015 3:13 am UTC
- Forum: Logic Puzzles
- Topic: Logic Puzzle
- Replies:
**2** - Views:
**2048**

### Re: Logic Puzzle

Because of the O - Y = O and H - R = H columns in the first subtraction, R and Y must be 0 and 9 in some order. By H - O = R in the final column of the second subtraction, R = 9 and O = 0 . By the last column, H + 1 = O and H + S = 10. Assuming all the letters represent a different digit (as is...

- Wed Dec 31, 2014 7:03 pm UTC
- Forum: Mathematics
- Topic: What is the biggest PWND you can get?
- Replies:
**10** - Views:
**2670**

### Re: What is the biggest PWND you can get?

It means "for any two points, there must be at least one other point in the set that isn't on a line connecting those points". The five points in the example set are (0,0), (3,0), (-3,0), (0,4), and (0,-4), so there are 2 points not on the x-axis, and 2 points not on the y-axis.

- Wed Dec 31, 2014 6:55 pm UTC
- Forum: Mathematics
- Topic: Numbers easy to factor
- Replies:
**40** - Views:
**5516**

### Re: Numbers easy to factor

That's the thing: you have to find a value that will work out of all the possible candidates, which devolves into factoring the number to begin with! Choosing k to create the largest possible triangular number that doesn't exceed the number to be tested (or, in the alternative formulation, the small...

- Wed Dec 31, 2014 6:42 pm UTC
- Forum: Mathematics
- Topic: Numbers easy to factor
- Replies:
**40** - Views:
**5516**

### Re: Numbers easy to factor

Because you're not choosing the right k value, of course! Just like if you try it with n=291: if you choose k=23, t(k)=276, r=15, but 23-15+1 = 9 is not triangular. Does that mean it's not composite? Well, if you try again with k=50, t(k)=1275, r=-984, then this time k-r+1 = 1035 will lead you to fi...

- Wed Dec 31, 2014 6:13 pm UTC
- Forum: Mathematics
- Topic: What is the biggest PWND you can get?
- Replies:
**10** - Views:
**2670**

### Re: What is the biggest PWND you can get?

It is trivial to create a Eudclidean grid of arbitrary size by picking a highly-divisible number, for example 60, starting with points (0,0), (0,60), and (0,-60), then finding several different Pythagorean triples with leg lengths that are factors of your number and putting all remaining points on t...

- Wed Dec 31, 2014 5:41 pm UTC
- Forum: Mathematics
- Topic: Numbers easy to factor
- Replies:
**40** - Views:
**5516**

### Re: Numbers easy to factor

Here is the example of n=109223 How do I know that this number is quickly to be factored? I compute n=t(k)+r where t(k) is a triangular number (k(k+1))/2 n=t(466)+412 I compute k-r=466-412=54 I check if 54+1 is equal to some triangular number 55+1=55=(10*11)/2=t(10) It is!!!! Then n=109223 is 100% ...

- Fri Nov 14, 2014 2:26 pm UTC
- Forum: Mathematics
- Topic: Help me with this equations please!
- Replies:
**13** - Views:
**4444**

### Re: Help me with this equations please!

This problem space reduces to "find B where sqrt(202B^2 - B + 10201) is an integer" (then A is simply the resulting integer plus 101), and from there the last digits of perfect squares allow us to rule out any B that ends in 1, 2, 6, or 7. Additionally, ending digits of 0, 3, 4, and 8 must...

- Sun Nov 02, 2014 9:05 am UTC
- Forum: Logic Puzzles
- Topic: A simple code idea
- Replies:
**19** - Views:
**5289**

### Re: A simple code idea

**Spoiler:**

- Sat Sep 27, 2014 10:12 am UTC
- Forum: Logic Puzzles
- Topic: Simple grid placement puzzle
- Replies:
**12** - Views:
**3285**

### Re: Simple grid placement puzzle

On the metric of minimizing the value, start in the corner square A1. The lowest candidate for that square is obviously 1, so plug it in. The only constraint that's placed on 1 is that it cannot be adjacent to 2, so the lowest number which can potentially occupy A2 is 3, so plug that in. Now bo...

- Wed Sep 24, 2014 5:17 pm UTC
- Forum: Logic Puzzles
- Topic: Simple grid placement puzzle
- Replies:
**12** - Views:
**3285**

### Re: Simple grid placement puzzle

Label the grid as follows: A1 A2 A3 B1 B2 B3 C1 C2 C3 Now the numbers 2, 4, and 8 all disqualify each other by factorization, so these numbers must be is separate rows and columns. With the long diagonals also serving as disqualifying lines, without loss of generality these numbers must occupy A2, B...