Logic Masters India announces September 2011 Sudoku Test — Crazy Arrows

Dates : 10^th and 11^th September

Length : 110 minutes

IB and Submission Link : http://logicmastersindia.com/M201109S/

Author : Rohan Rao

This looks like a lot of fun -- interesting variations on a common theme.
One thing that strikes me as worth clarification: The arrows in "Mirror Arrow Sudoku" aren't strictly mirror images of each other at all. The puzzle has the usual 180-degree rotational "crossword" symmetry, and the arrows follow that symmetry (assuming that the puzzle will follow its example in the booklet). That's the sort of thing that could be very confusing to somebody reading the instructions on the day of the test without carefully studying the instruction book. It may be better to call this one Symmetric Arrow Sudoku.

Yes, the circles and the arrows have the usual 180-degree rotational symmetry. And 'Symmetric' is a better name, I wonder why it didn't strike me earlier.

Updated IB with change in name uploaded.

Lots of math puzzles! I'm really looking forward to this test.
I have some questions about Symmetric Arrow Sudoku.
What is the definition of "arrow"? More precisely,
1. Length: Can the length of arrows be 1?
2. Directions: Only 8 directions?
3. Only one arrow from each circle?

For Missing Arrow Sudoku:

Only one circle and one arrow tip should be placed for each line or we can place circle somewhere into the middle of the line (to create circle with two arrows)?

One end should be an arrow tip, and other end should be the circle.

Circle in the middle is not allowed.

I had the same question . The example in the IB is not easy, considering you can have arrows of length 1 (but still have a unique solution).

Fred

I think I can answer this question:

Consider a such grid where you have more than one arrow from each circle. Then, if you remove one arrow from that circle, it's also a valid grid, but perhaps it has more than one solution considering the starting configuration. If so, the entire problem will have more than one solution. Rohan cannot ask us to add some additional arrows to avoid the fact that the grid has more than one solution...

Therefore the grid must have a unique solution with a unique arrow from each circle .

I don't know if I'm clear, it's a bit hard to explain in English...

Fred

Nice explanation, Fred. I think you are right. Something else I noticed in this puzzle. In the example the middle circles may collect the numbers in two possible ways. I don't know is this counts as unique or double solution. The numbers are surely unchanged but maybe it's not bad to know does the same case can appear in real puzzle.

Nikola

Edited by Nikola 2011-09-07 5:22 PM

Thanks, Fred. Everything is clear. And I noticed the same point as Nikola.

Regarding Symmetric Arrow Sudoku:

1. There is one unique arrow from each circle. This arrow must have a 180-degree symmetric arrow from the opposite circle. Fred's earlier post is absolutely correct.

2. There CAN be arrows of length one.

3. In the example, the middle circles can collect its numbers in two ways. The '9' can collect 4-5 and 5-4 (Similarly, the 1-3 and 3-1 for the '4'). But, the solution does not change and both ways is considered to be the SAME SOLUTION. As long as you collect the numbers from the same cells, the arrows are the same, irrespective of the order/direction.

4. No part of an arrow can go outside the grid. It can travel only through centres of neighbouring cells (in standard format), i.e. it can go in any of the 8 directions, but it cannot touch/cross the grid border.

5. I should've put a better example in the IB :-)

(I will create one more example of Symmetric Arrow Sudoku and post it by tomorrow, it should be clearer then)

Edited by Rohan Rao 2011-09-07 6:24 PM

For 0-9 Arrow Sudoku:

1. Can a circle have more than one arrow?
2. If so, can the sum change over the different arrows? Say, a circle has the digits 1 and 2 in it, can one arrow sum to 12 and the other sum to 21?

I was wondering this because the instructions says both orientations would be considered correct. And I would assume if the sum of each circle is unique, it would be more logical to just accept only the correct sum for the circle as an answer. My other idea for the reasoning would be that some circles have their digits given, but not necessarily in the right order and people might forget to change it when putting in the answer key.

0-9 Arrow Sudoku
--------------------
Each circle will have exactly one arrow.
Circles won't have givens, if that helps.

I think Rohan wanted to clarify that while entering the answer, one can enter the 2 digits in the circle in any order.

Each circle has exactly one arrow. That should solve the problem now. Of course, you will get a unique order of the two digits inside a circle while solving.

Both orientations are accepted as correct 'answers' just for convenience of players. As long as you get the two correct digits in the circle, it is ok for me. For example, an arrow over two cells may have 0 and 8 in its circle. The sum is obviously not 80. So, even if a player types '80' instead of '08' (maybe due to quickly typing it from the paper), it is as good as correct.

Here is a fairly easy Symmetric Arrow Sudoku that you can try out:





Solution:

If X submits 11 correct sudokus and 13 digits correct in the last sudoku, and one of the five wrong digits is a given clue. Does X get the time bonus ?

Edited by rakesh_rai 2011-09-09 4:22 PM

Yes, of course.

Password protected booklet uploaded. It has 12 pages, each page one Sudoku. There is no cover page.

nice set of SUDOS!!! (it was really CRAZY)
I dont know what happens to me while having sudoku test..
kinda find difficult to solve any sudoku..
Just missed submitting my sum1 sudoku answer.
but anyways it was nice experience
surely i need lots of practise to get command on sudoku.

Thanks for the puzzles Rohan

awesome puzzles Rohan......the arrows have really made me crazy!!!!

Thanks Swaroop, flk and Neeraj. A lot of people have gone crazy due to different reasons :-)

Excellent test, really had fun solving :) Unfortunately I made the awesomely horrible mistake of forgetting to click "submit answers" after half time :P But really enjoyed it. especially missing arrow Sudoku, which was quite confusing.. :P