Welcome to the forum.

There is an entire "family" of straight lines where 7x+ 11y = something.

They are all parallel and as N gets bigger the lines move away from the origin. Joining (11,0) to (0,7) will produce one. What is N for this case?

That should give you a starting point.

Bob

]]>**Welcome to the forum.**

Some puzzlers like to make a simple thing complicated just to make it hard. The "As I was going to St Ives" puzzle is an example.

So is Lemonink.

The amount transferred is irrelevant. Let's say we have a glass with 100mL lemonade and a second with 100mL of ink.

Start tipping liquid from one to the other in any way you like and as many transfers as you like. Stop when the first glass has exactly 100mL of liquid in some mixture. There's no way we can know how much is lemonade so let's say it has x mL of lemonade. As it has 100 altogether there must be 100 - x mL of ink.

The second glass must also have 100mL altogether as long as we didn't spill or drink (!) any. How much is lemonade? Well we know where x units is so the second glass must have 100 - x mL of lemonade. And as there are 100mL altogether in that glass there must be x mL of ink.

So in the first glass lemonade : ink = x : 100-x and in the second ink : lemonade = x : 100 -x

I did read your explanation, but I got totally lost half way through. Sorry.

Bob

]]>3 - 0! + 0 + 5 + 6 = 13

]]>Tommy opens his bottle and begins drinking the soda. But when I open my bottle, it was frozen solid. I complained.

What happened?

]]>You've posted this as an exercise, but you've made it seem more like a help me problem. There's a difference: If it's an exercise, then members have a go for fun and maybe just post an answer. If it's a help me, then much more explanation would be provided and the 'student' encouraged to do some / most of the working themselves. Please clarify.

Bob

]]>Of course, I could be wrong... but it's a place to start. Let me know if you find it.. I will be unlikely to get to Beijing again to try it.

]]>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

]]>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.

]]>