its cool but just a bit confusing at first.

I was wondering if I should put some explanatory text or something showing how to play. thank you very much for your feedback

]]>i have a pi puzzle (actually a pie day puzzle)which i cant solve. I hope you can help me with this .

https://www.geocaching.com/geocache/GC721K1_dozens-of-pies

The Hint for this puzzle is

[Puzzle]: [ Put some dozen Pies in your shopping cart,

check them all out and you pay only the integer part of the total price.

Don`t forget counting your money before paying! ]

(check, integer, counting, failure)

At the Endresult must be some coordinates for example like this:

N 39° 52.935` E 116° 24.397`

Dozens of Pies is the headline. So i think it is about the digit pi.

The name pie is just a metaphor for pi.

Prize for one pie is pi

And you only count only integer number

So i started like this dozens of pi

x *12 * pi = 37.6991118431 (multiple of Pi * 12)

But the i dont now how to continue.

check them all out is the main key of the puzzle

The endresult must be some coordinates for example

N 39° 52.935' E 116° 24.397'

Can u please help me to solve it ?

Kind regards philip

ONE:

400:

169,196,961:

9+0:

9-8:

10-9:

81-0:

6^0, 8^0, 9^0, 10^0:

6/6:

8/8:

9/9:

Here are two options that, by making one change to the puzzle in post #6, converts it from unsolvable to one that has a unique solution:

```
Option 1: C1 empty Option 2: G1 empty
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
A | _ 2 _ | 1 5 _ | _ _ _ | A | _ 2 _ | 1 5 _ | _ _ _ |
B | _ _ 5 | 2 _ _ | _ _ 9 | B | _ _ 5 | 2 _ _ | _ _ 9 |
C | _ _ _ | _ _ 4 | _ 2 5 | C | 3 _ _ | _ _ 4 | _ 2 5 |
|-------+-------+-------| |-------+-------+-------|
D | _ 8 7 | _ _ 2 | 5 _ _ | D | _ 8 7 | _ _ 2 | 5 _ _ |
E | _ 4 _ | _ 1 7 | _ _ _ | E | _ 4 _ | _ 1 7 | _ _ _ |
F | _ _ _ | _ _ 3 | 1 _ 7 | F | _ _ _ | _ _ 3 | 1 _ 7 |
|-------+-------+-------| |-------+-------+-------|
G | 2 _ 4 | 6 _ _ | _ _ _ | G | _ _ 4 | 6 _ _ | _ _ _ |
H | 6 _ _ | _ 9 _ | _ 3 _ | H | 6 _ _ | _ 9 _ | _ 3 _ |
I | _ 5 _ | _ _ _ | 9 6 8 | I | _ 5 _ | _ _ _ | 9 6 8 |
```

Both solutions are easy to find, and are different from each other.

]]>computer runs at about 140,000,000 steps/second, that would take something like 10^18 years. However the constraints reduce this dramatically, so that the whole process only took 470 seconds !

I just use visual basic in Excel, so lower level languages like C++ would no doubt be even faster. The trick is to pick your blank cell loops so that you can use a 30ish cell sum constraint as soon as possible.

I first came across this type of puzzle in a Sudoku forum that I am in, where someone could not solve one of these problems with the first and last rows being completely specified (in addition to the nine 30ish cells).

Well I just love a programming challenge and I looped through the 28 unspecified cells, and found the unique solution in less than perceptible time.

To find other similar puzzles I just did a google search and eventually found this thread, which naturally suggested the 40 blank cell problem which obviously would have multiple solutions.

]]>The hour and minute hands are at equal distance from the 6 hour, what time will it be exactly?

There are 12 solutions where the two hands are on different sides of the clock face, and the distance to the 6-hour mark for one is measured in the reverse direction to that of the other.

There are 11 solutions where one hand is on top of the other and the direction to the 6-hour mark for both hands is the same.

EDIT: I've had another think about this, and I reckon that although the puzzle wording doesn't say so, we're probably just meant to give the exact time of the clock hands shown in the image on the puzzle page (and reproduced below)...in which case there's only one solution. It doesn't really make sense otherwise, there being so many solutions.

]]>

I have an answer, and it is one of the six possibilities you listed.

]]>

Your solution is correct. It is one of two solutions to the puzzle with its current revised wording, which was a failed attempt in June 2012 to produce a single-solution version after it was discovered that the original wording had multiple solutions.

Puzzles like this typically have just one solution, and the fact that there are more has attracted quite a bit of discussion on the forum in several threads.

Here is a link to the most recent discussion. It also contains the latest revision (see below), to which there is only one solution. It was first posted 3 Feb 2013, here, but hasn't made its way to MIF's puzzle page.

1. The person in the middle watches Desperate Housewives

2. Bob is 46

3. The person who watches the Simpsons is next to the person who lives in a youth hostel

4. The person going to Africa is behind Rachael

5. The person who lives in a village is 52

6. The person who is going to Australia has straight hair

7. The person travelling to Africa watches Desperate Housewives

8. The 14-year-old is at the end of the queue

9. Amy watches Eastenders

10. Eilish doesn't live on a farm

11. The person heading to Italy has long hair

12. Keeley lives in a village

13. The 46-year-old is bald

14. The fourth in the queue is going to England

15. The people who watch Desperate Housewives & Neighbours are standing next to each other

16. The person who watches Coronation Street stands next to the person with an afro

17. The 21-year-old lives in a youth hostel

18. The person who watches Corrie has curly hair

19. The 81-year-old isn't going to England

20. The person who is travelling to France lives in a town

21. A person next to Rachael has an afro

22. The person who watches Neighbours has long hair

Maybe you'd like to try it!

]]>Looks formidable, math notation is rather clumsy and seems to be designed to confuse rather than enlighten, but it is easy to solve computationally. We check the coefficient of x^85 and find that is 7, meaning there are 7 solutions to this.

We can also use Bezouts Identity:

From the first solution (27,1) this reduces to

now we only have to apply k = 0, -1, -2, -3, -4, ... to get all the solutions:

{3, 19}, {7,16}, {11, 13}, {15, 10}, {19, 7}, {23, 4}, {27,1}

]]>The number they want next is

.Welcome to the forum.

]]>