Math Is Fun Forum

Hi Checker 555!

I went to the Checkers game, and also got a pop-up that prevented play.

However, my pop-up has a 'New Game' button at the bottom, and clicking that makes the pop-up disappear and starts a new game.

The pop-up also has a 'Close' button next to the 'New Game' button, but clicking that only closes the pop-up. To start a game you'd then have to click the 'New Game' button above the playing board.

I hope your pop-up's the same as mine!

Hi Bob...the guitarist is Gerhard Gschossmann.

And here's the link to the recording I used: Gerhard Gschossmann - 'Summertime' (George Gershwin) guitar solo fingerstyle

That version is played at the song's correct tempo, with good feeling and expression...which makes my Geogebra soundtrack sound rather chipmunkeyish.

Here's a vocal clip of the song: GEORGE & IRA GERSHWIN 'Summertime' HAROLYN BLACKWELL ('Porgy & Bess'). Very moving!!

Hi Bob,

Here's a little video of an animation of the range of non-symmetrical scenarios obtained by running Point B along line AP:
Non-symmetrical range (video)

Edit: Sorry, I lied.   The range includes the symmetrical scenario I mentioned in my previous post. The symmetry appears 3 times: at the start of the video, at the 14-second mark, and at the end of the video. Each time, N is smack in the middle of the square and the 4 vertices are 67.5°.

Hi Bob,

I suspect that making a square with those extensions will help!

I've redrawn the diagram:

It also 'happens' that PO runs through N...and, of course, PO divides right angles APD and DOA into 45s.

...and there are umpteen similar triangles (but I haven't seen anything yet).

Thanks, coolboyx12.

I resign!

...not that I think there's anything wrong with the thoughts I've presented!

Thanks, coolboyx12.

So I've looked at ganesh's method, and have some comments about it:

A. Depreciation:
The problem doesn't mention depreciation, nor its percentage, but ganesh's method includes a yearly fixed depreciation rate of 10%, applied to 3 years.
   1. There seems to be no generally-used standard regarding the amount of vehicle depreciation: instead, the depreciation percentage depends on many factors, such as the make and model of the vehicle, its age and its use (eg, private or business).
   2. Vehicle depreciation rates are not necessarily fixed (eg, diminishing rates).
   3. If we assume that depreciation applies, it's important to know when it takes effect: eg, whether it's at the beginning, or at the end, of each year (often a vehicle's value depreciates immediately a person takes possession of it). If applied at the start of each year, it should be applied in each of the 4 years, not just the first 3 (the damages claim was in year 4).

B. Insurance premiums:
There are 4 insurance terms ('After 3 years he got a claim of damages'), but ganesh's method only charges for 3.
   
Another thing unclear to me is the huge discrepancy between the initial worth of the vehicle (Rs. 450,000) and the subsequent 'claim of damages' (Rs. 750,000).

To me, it implies that the initial worth (unadjusted over time) was simply used as a basis for premium calculation, and that the insurance policy actually covered a higher amount.

Hi coolboyx12;

Edit: On re-reading the question, I've come to the conclusion that I don't understand the question at all! So maybe you should ignore what I wrote in the hide bar.

I'll think about it some more, but there seems to be some critical info missing...

Hi tony123;

Too tough for me, so I tried trial and error in Excel and got this:

Hi jiaoqian, and welcome to the Forum!

I did this puzzle many years ago, and, like you, could not resolve the French/Brazilian cocoa/tea issue.

That means there are two solutions, which, for me, is disappointing.

I've done many of these types of logic puzzles, and the Ships Puzzle is one of the very few I've come across that has multiple solutions...

Hi;

I thought I'd try Excel's Goal Seek, and managed to solve this thread's cubic and a couple of others I tested it on:

The two extra cubics have 3 roots each, and to find them I entered into column D the initial x values that I'd predetermined and stored in Column C, those values being:
(a) a high initial value to try to find the highest x;
(b) a low initial value to try to find the lowest x;
(c) half the sum of the resulting highest & lowest x values from (a) & (b) to find the remaining x (not sure if that's a good idea generally, but it worked for these equations).

Then I ran Goal Seek (individually for the equations in rows 2, 3, 5-7 & 10-12) with the respective Goal Seek boxes filled from columns E & D as per the image example.

Btw, to increase Goal Seek's precision (quite a necessary step for good accuracy with this method), I first set 'Maximum Change' in Excel's File/Options/Formulas/'Enable iterative calculation' to 0.000000000000001, which gave accuracy to 14 decimal places for this thread's cubic: i.e., x ≈ -2.09144638072228 (the last few digits aren't displayed in the image).

The above cubics are the only ones I've tried this Goal Seek method on...

Yes, I can...as part of the following Imgur web page (a screen capture):

However, while your link works for me now, I've found from your other posts that your web page links only work for a limited time, if at all.