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#1 Re: Help Me ! » Annuity, regular investment calculation - formula needed! » 2015-03-25 11:31:07

Hi Andrew,

It may be worthwhile to learn the general formula I gave as it could help deal with a tricky exam question. smile

#2 Re: Help Me ! » Annuity, regular investment calculation - formula needed! » 2015-03-25 02:45:38

Hi Andrew1930,

Yes, great answer from Bob with those workings! Even I understood them! smile

I found this formula on the net:


Where:
P = principal after n years
M = deposit amount per period
i  = annual interest rate
q = number of equal time periods per year
n = number of years

Because q=1, the formula simplifies to Bob's.

This formula may be of interest for tackling other problems: eg,
M = $250 deposit at the end of every six months
i  = 6% annual, but interest calculated six-monthly
q = 2
n = 5

Answer: P = $2865.97

Annuity.png

#3 Re: Puzzles and Games » Mate in 15...or less? » 2015-03-24 10:12:58

Sorry about the confusion, stefy...I've fixed the wording.

#5 Re: Puzzles and Games » Mate in three? » 2015-03-23 23:52:57

Agnishom wrote:

1. Rh1 Rf8
2. Rh3 Rd8
3. Rh1 Rf8
4. Rh3 Rd8
.
.

Black would be very pleased indeed if White went 5. Rh1! smile

Agnishom wrote:

There are also many ways to iterate the game infinitely

'Infinitely' is not possible these days under FIDE Laws of Chess.

#6 Puzzles and Games » Mate in 15...or less? » 2015-03-23 21:35:17

phrontister
Replies: 5

Hi;

I saw this on another forum, from a 2012 thread:

Mate-in-15_or_less..._.png

Posters on that forum solved it as a mate-in-15 with Critter 1.4, Stockfish 2.2.2 (both freeware) and Houdini 2.0c (commercial).

Without thinking about this properly I entered the position into some freeware chess engines I have, seven of which found mate in much less than 15:

     Engine         |          Time
------------------|-----------------
Houdini 1.5a     |      0.08 seconds
Critter 1.6a       |      1.36 seconds
Fire 4.0            |      8.44 seconds
Stockfish 6       |      9.94 seconds
Gull 3               |    15.21 seconds
Komodo 5.1r2   |    31.71 seconds
Rybka 2.3.2a    |  273.63 seconds

A couple of others didn't find mate in any number of moves after about 5 minutes (which I thought was long enough for them to think), and so I gave up on them.

Looking at this puzzle again (with the benefit of hindsight, I know), I'm sure that a human solution for mate in much less than 15 moves isn't all that hard to find.

So...what is the least number of moves you can find for White to mate?

White's pawns move up, Black's down, and White moves first.

The rules: no chess engine help!

Please hide your answer, in which I'd like you to include the moves line (I think there's only one optimum line) and your reasoning.

smile

#7 Re: Puzzles and Games » Mate in three? » 2015-03-23 20:26:39

There are also many ways to iterate the game infinitely

Sorry, Agnishom, but I don't know what you mean by that.

#8 Re: Puzzles and Games » Mate in three? » 2015-03-23 13:26:21

Oops! Thanks, stefy. I'd placed White's Nf6 on Ng6. >{blush,grumble}<

Yes, Black can't prolong the game beyond mate-in-3 with White = 1. Qb5 (as per SteveB). I tried all possible options.

#9 Re: Puzzles and Games » Mate in three? » 2015-03-23 12:42:02

1. Nxb3+ Kd5
2. Nxd2+ Rc4
3. Bxc4#

In this variation Black's king is forced by two discovered checks to move to safety himself because White's checking pieces (first the queen, then the bishop) cannot be captured and Black has no blocking pieces with which to shield the king from them.

Other than the above, the Black king's only move option is on his first move: ie, Kc4...but that leads to mate-in-2 with Nxd2#.

#12 Re: Maths Is Fun - Suggestions and Comments » Link to mathsisfun.com » 2015-03-12 22:59:13

Hi Chris2,

I don't recall there being such a link on the forum, but that probably only tells you how good my memory is!

I knew about the mathsisfun-to-forum link and I thought there might have been one for the other direction.

Thanks.

#13 Maths Is Fun - Suggestions and Comments » Link to mathsisfun.com » 2015-03-12 19:37:59

phrontister
Replies: 2

Hi;

Is there a link somewhere on the main forum page or header to mathsisfun.com?  I can't find one.

On my browser I have a bookmark to the forum, and sometimes when I'm there I'd like to be able to just click a link on a forum page to take me to mathsisfun.com.

Or maybe I could just add another bookmark to the browser toolbar...

#14 Re: Puzzles and Games » The Garden Problem » 2015-03-04 03:38:08

Hi patdools,

Well, I solved it with 'IN'. :)

However, the reasoning turned out to be much the same as for 'PoE' because of the puzzle's unusual trick of having multiple varieties per crop. 'IN' seemed to me to be rather difficult to express in concise terms at times, so unless you want to grapple with that issue I'd recommend you use 'PoE'.

I've redone post #4's worksheet and have made it suitable for either strategy. The special work area for clues 4, 5 & 6 that I included in that earlier worksheet isn't necessary, so I've omitted it. Also, not all clues are needed to solve the puzzle: the solution route I take for both strategies doesn't need clues 5, 9 & 10, which I've marked as being superfluous.

The hidebox contains the new worksheet image, and you can choose which strategy to use:
(a) 'IN': ignore the four rows under the row beginning with "Position". Here is a link to an 'IN' info post.
(b) 'PoE': scan the clues (maybe multiple times!) and eliminate false entries from the grid containing the bold capitalised letters. Here is a link to a 'PoE' info post.
(c) Both strategies: enter solutions into the blank grid and your reasoning into the ruled section below the yellow highlighted row.

I enter the reasoning in numbered list form to aid with reviewing and referencing the content...which can also help to troubleshoot a blunder. The yellow highlighted line contains suggested notations for keeping entries concise.

You may prefer to set up your own spreadsheet for the benefits it gives, but a printout (preferably coloured) can be used away from the computer.

Enjoy! :)

#15 Re: Puzzles and Games » The Garden Problem » 2015-03-03 04:28:25

Hi patdools,

While I solved this puzzle using the 'process of elimination' ("PoE") method I referred to in post #4, I think that Bob may have converted me over to using the 'insightful narrative' ("IN") method I described here.

'PoE' is generally the quicker of the two, but, as Bob said, it takes away some of the thinking. Solving it by the 'IN' method will most likely give you greater satisfaction, and I'd recommend going that way.

In fact, I just finished drawing up an 'IN' worksheet (in Excel) and am looking forward to giving that method a go. smile

Bed time first, though...

#16 Re: Dark Discussions at Cafe Infinity » Words that contain AEIOU, in any order, each vowel exactly once » 2015-02-27 21:23:03

Hi Olinguito,

countenacing

That should be 'countenancing'.

OUEAI:
connumerating
counterbracing
countercharming
counterclaims
counterdrawing
counterraid
counterraids
counterrallying
countershadings
counterstains
counterstating
countertactic
countertactics
countertrading
countervails
documentalist
documentalists
documentarist
documentarists
groundbreaking
groundbreakings
housemaids
housewarming
housewarmings
monumentality
mountebankings
mountebankism
mountebankisms
mousetail
mousetails
mousetrapping
noumenalism
noumenalisms
noumenalist
noumenalists
noumenality
outbeaming
outbleating
outbreaking
outbreathing
outcheating
outdebating
outdreaming
outearning
outfeasting
outgleaming
outhearing
outleading
outlearning
outpreaching
outreading
outscreaming
outswearing
outwearying
pronuclearist
pronuclearists
protuberating
routemarching
souterrain
souterrains
troublemaking
troublemakings

Italicized words are those in Agnishom's large general listing in post #31, but I've included them here under the OUEAI heading.

The others haven't appeared in the thread so far...and all words are in the Collins English Dictionary.

#17 Re: Help Me ! » Need some help with transformations problems » 2015-02-26 21:51:57

So, after sorting symmetries and ratios, I got:

#19 Re: Help Me ! » Need some help with transformations problems » 2015-02-26 20:19:12

Hi SPARKS_CHAN,

For #2 I get 5, as per image:

LaserInSquareDistance.png

What I don't know (and I've only done this graphically in Geogebra), is how to prove that the laser terminates at D.

#20 Re: Help Me ! » Meet this Challenge » 2015-02-22 00:21:49

Hi Christy,

I already have it on a chart, with all the eight names...

I guess you mean the eight surnames. I may be wrong, but I reckon you'll strike trouble doing it that way. I think a better choice would be to focus on the 16 first names.

Can you please give me a hint...

Coming right up! smile

See can see from our posts that there are several different strategies for solving this puzzle. In my previous post I gave the reason for preferring the 'insightful narrative' method (that's just a term I made up), but of course the choice is yours.

Here's a start for you (see image) if you want to use that method, and I'll explain some things about it and give you some tips...

The yellow highlighted entry in the first line of the 'solutions list' column to the right of the clues is just an explanation of notations I use throughout the reasonings in the list. The notations help keep the wording concise so it all fits better per line, and they also help to identify info when scanning the clues list and the solutions list while working on a solution.

The "{x}" notation (where "x" stands for the item number in the solutions list) is useful when, in subsequent list entries, you want to refer to solutions already found.

Below that first line I enter all the reasoning used to solve the puzzle.

I think it's important to begin with entering all the obvious solutions you can find in the clues for each person. I've given two such solutions for the first item in the list (there are several more, but I'll leave them for you to find):

"1. Fill obvious given solutions for each person from clues [1], [3], etc".

The "[1]" and "[3]" refer to clues 1 and 3, and I've entered the solutions onto the grid in the image.

Of course, for clue 1 we can only enter the answers into Daniella's cells at this early stage and not into her husband's, as we don't know yet who he is. When we find that out, all his details and Daniella's should immediately be shared between them.

You'll need to identify the composition of all eight couples, and I'd recommend aligning husbands with their wives as soon as possible. I number the couples C1 to C8.

Aligning is easily done in a spreadsheet by relocating the grid cells involved, but other tactics can be used too: eg, numbering the couples, or shading the cell containing their first names with identifying colours. I align and colour, as you'll see in the image for the next item in the list:

"2. C1=Owen & Victoria, who like brown[3]".

Compare the image below with the one in my previous email to see what I've done re the following:

phrontister wrote:

I used Excel to help with visual aids, such as to:
(a) move husband/wife cell groups to align solved couples;
(b) grey out solved clues;
(c) fill the cell of used-but-not-solved clues with a light colour (eg, pale yellow).

Worksheet_-2.jpg

Keeping a clearly notated list of your solutions to which you can refer will help with troubleshooting (should the need arise), and can avoid having to make a complete restart following a blunder!

All the best with this! smile

#21 Re: Help Me ! » Meet this Challenge » 2015-02-18 16:31:15

Hi Bob,

I don't like to use that method as it seems to take away a lot of the thinking...

Yes, I'd agree that the 'process of elimination' method I gave links to in my previous post does reduce the amount of thinking required. It's faster, but even so usually still needs a fair bit of reasoning...as I found with this puzzle, which had a couple of tricky spots.

Stung into action by your observation wink, I thought I'd have a go at solving the puzzle via the 'insightful narrative' route, such as the kind you'd find in the Solutions section of Logic Puzzles books.

I did away with the usual working grids and drew a grid in Excel for answers only, with a large blank section to the right of it for entering my reasoning...in numbered list form. To help speed up scanning and locating info, I used bold coloured text in the clues...also in the grid headings.

I used Excel to help with visual aids, such as to:
(a) move husband/wife cell groups to align solved couples;
(b) grey out solved clues;
(c) fill the cell of used-but-not-solved clues with a light colour (eg, pale yellow).

I took off like a rocket on the easy stuff, but quickly slowed right down when the time came to think! Eventually got there, but not as insightfully as I would've liked. The experts seem to have a knack for this...

Anyway, I got greater satisfaction this time around than with the 'speedy' method.

So...thanks. smile

Worksheet.jpg

#22 Re: Help Me ! » Meet this Challenge » 2015-02-14 13:29:37

Hi;

I solved the puzzle this morning. It's quite long, but nice and challenging...and there's just a single solution.

For these types of logic puzzles I use the method described here.

And here is a link to my worksheet layout and comments re the "Who lives in the city?" puzzle. The worksheet will need to be adapted to suit this puzzle, of course...which is half the fun!!

Hope that helps. smile

PS...Re the two challenge questions:
(a) "Who likes Violet?"......The couple to whom that refers can be determined well before the end.
(b) "And can you find out everything about everyone from this?"......Yes.

#23 Re: Exercises » Restricted partitions » 2015-02-12 19:20:12

Oh...I'd seen that thread but forgot about it because it went over my head, and I didn't link this one with that.

Sorry, but all this looks too advanced for me. I've never done GFs and don't understand the concept.

#24 Re: Exercises » Restricted partitions » 2015-02-12 18:58:47

But where to start looking! I need to have some idea of the solving technique before I begin.

I've worked out (I think) how to solve the puzzle 'with replacement' (answer 24704), but that's as far as I've got. All I can think of for a 'without replacement' solution is to program a simulation, but that wouldn't give an exact result.

#25 Re: Exercises » Restricted partitions » 2015-02-12 18:40:56

I see.

That means each time a number is removed the number of options from which to choose reduces by one, so that the last number chosen is from a group of 15 numbers.

I think the task is to find the number of different chosen groups there would be that sum to less than 61.

Hmmmm. I think that's beyond me.

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