TurkZeka 2007/2 Puzzle Competition


CHAIN OPTIMIZATION



Create the honeycomb chains by painting the adjacent honeycombs
at the platform above with the different colours.
The chains must have at least three honeycombs.
Each honeycomb which forms a chain can have two neighbours at maximum.

WRONG CHAIN WRONG CHAIN WRONG CHAIN VALID CHAINS

WARNING: If two different chains are connected with each other according to chain rules, they must be counted as one chain. And the numbers must be placed according to this.

Namely; You cannot separate the chain which has 7 honeycombs(For example, triple and tedrad chains). Otherwise both of these chains will be invalid.

The wrong chains in your solution don't invalidate your solution. But, the honeycomb numbers at these chains don't be added to your score as a positive multiplier. Besides, the honeycombs numbers affect your score as negative (ullage).

3 examples to this warning:

VALID CHAINS
The chains with
4, 4 and 11 honeycombs

INVALID CHAINS
Only two blue chains are valid.

VALID CHAINS
The chains with
3, 3, 3, 4
and 5 honeycombs

After than; Place the numbers which are 1 to 9 into the honeycombs in the main diagram with the rule that there must be each numbers at least once.

THE RULES:

1) There must be numbers at two honeycombs of each chains you created at least. And sum of these numbers must show the honeycombs numbers in that chains. For instance, you cannot place number 5 into the only one honeycomb of a chain which have 5 honeycombs. You can place the numbers into the honeycombs as 1- 4, 2 - 3 or 1 - 2 - 2.

2) There can be numbers at maximum two of six honeycombs which are adjacent neighbour of one honeycomb which has number. And these numbers cannot be adjacent.

3) There cannot be same number at none of the honeycombs where the directions of six edges of a honeycomb which has number.

INVALID PLACEMENT

INVALID PLACEMENT

INVALID PLACEMENT

 

VALID PLACEMENT

VALID PLACEMENT

4) The numbers placed by not obeying the rules about the number placement will make your solution as invalid. So you will get 0 (zero) point from this puzzle.

5) The honeycombs which cannot create a chain will be accepted as ullage. The honeycombs which form the chains whose honeycombs numbers is not equal with the sum of the numbers on it will be accepted as ullage. The honeycombs which form the chains formed by not obeying to the rules about the number placement will be accepted as ullage. These ullages will decrease your score.

SCORE CALCULATION

You will calculate your score by multiplying the honeycombs numbers of the chains which you create. If you have not more than one ullage, this score will be your real score.

If your ullages are more than one; you will calculate your real score by subtracting 6 base of your ullage number from your score.

For instance, if you have 2 ullages; 2 x 2 x 2 x 2 x 2 x 2 = 64 will decrease your score.

WARNING:

Paint the honeycomb you determined as ullage, with black colour. You cannot place number into the honeycomb you determined as ullage. If you don't paint the ullage honeycombs with black colour, that chain will be completely invalid. So, the honeycombs which form that chain will decrease your score.

3 examples to this warning:

SCORE: 6 - 4826809

SCORE: 6 - 4826809 SCORE: 6 x 12 = 72

Analyze the score calculation and the sample solutions carefully.

If the puzzle was asked for the numbers 1 to 4, you would calculate your score like the examples' score calculations below:

INVALID SOLUTIONS: 0 point

    (There isn't number 3.)

 

VALID SOLUTIONS:

SCORE: -15576
(7 x 7 - 15625)
SCORE: 83
(7 x 7 x 3 - 64)
SCORE: 189
(7 x 9 x 3)

IMPORTANT: If sum of the numbers on a chain is less than honeycomb numbers, that chain will be invalid and real honeycomb number at the chain will be accepted as ullage. However, if the sum of the numbers on a chain is more than honeycomb numbers, the sum of the numbers will be accepted as ullage.

Ullages are calculated for the total of the whole ullages at the platform. (Not one by one for each chains)

ATTENTION! THERE IS BONUS!

After the calculation of your score, check the numbers you placed. If the numbers form a number chain by obeying the chain rules, you will get bonus and you will add this bonus to your score.

But, in order to get the bonus, the chain must be formed with at least 6 numbers.

You will get the bonus as much as "(Product of the numbers at that chain)" , from the number chains which are formed with 6, 7 or 8 numbers.

You will get the bonus as much as "( Product of the numbers at the chain ) x ( Number count at the chain )" , from the number chains which are formed with 9, 10 or 11 numbers.

You will get the bonus as much as "( Product of the numbers at the chain ) x ( Number count at the chain ) x ( Sum of the numbers at the chain )" , from the number chains which are formed with 12 or more numbers.

IMPORTANT WARNING: The bonus obtained cannot be more than main score! If your bonus more than your main score, your total scor will be calculated by equalizing your bonus and your main score.
Look at the examples to the bonus below. (Expecially the last example!)

3 Examples to BONUS:


 

MAIN SCORE: 3 x 5 x 5 x 6 = 450
BONUS: NO
TOTAL SCORE:
450

Bonus < Score


 

MAIN SCORE: 3 x 5 x 5 x 6 = 450
BONUS: 3 X 2 X 4 X 2 X 4 X 2 = 384
TOTAL SCORE: 450 + 384 =
834

Bonus < Score

MAIN SCORE: 3 x 5 x 5 x 6 = 450
BONUS: 2 x 3 x 2 x 4 x 3 x 2 x 9 = 2592
TOTAL SCORE: 450 + 450 = 900 (Not 450+2592)

Bonus > Score : Total Score = 900

For instance, if you create a chain which fits to the rules and has 12 numbers, like 1-2-1-3-1-4-2-5-7-3-1-6;

2 x 3 x 4 x 2 x 5 x 7 x 3 x 6 = 30240

1 + 2 + 1 + 3 + 1 + 4 + 2 + 5 + 7 + 3 + 1 + 6 = 36

You will get bonus as much as "30240 x 36 x 12 =  13.063.680"!

EXTRA BONUS !! (FORCE THE LIMIT OF YOUR INTELLIGENCE!)

If your number chain is formed with 12 or more numbers and if there are the numbers which are 1 to 9 (there must be at least one number for each number 1 to 9) at this chain, add 10% to your total score you calculated with your bonus points!!

Enter your total score as answer.
 

After you had entered your score, whether in the 24 hours solution sending period or whether you do not satisfy with your sent score and you had reached to the better one,
if you need you can send your new score with the solution file by using your second answer right. If you need you can use your third answer right with the same rules.

 

New Rule: The solution file cannot be sent after the deadline.
So, the competitors who entered the answer at last hours of the last day must remember that the solution file should be sent before at 00:00:00.

However, in your second answer, the sending day and the time of your answer
and the solution file will be taken to calculate your point and including your bonus points you will get %5 decreased points of your gained total points.

Also, in the same way, if you sent your third answer you will get %10 decreased points of your gained points which will be calculated according to the sent day and time of your solution.

Sending answer rights are limited with 3.
And no matter your last score is greater than the previous ones only the last answer will be taken to calculate your point.
Therefore, you should think of the advantages and the disadvantages of sending one more answer.

IMPORTANT!
Also you are supposed to email your solution to either
turkzeka@turkzeka.com
or yilmazekici@gmail.com after entering your answer within 24 hours.
You may send your solution in any common format such as image, Excel, Word.
Add your user name, password and the answer that you entered to your solution as well.
If you do not send your solution within 24 hours and/or do not add these required info,
your answer will not be accepted.

POINTS:
The owner(s) of the best score will be rewarded with 200 points, and others who achieve
to find
more than 2/5 of the best score will be rewarded according to the
ratio based on the best. (If the best score is 100, 41 will be required in order to be rewarded)

"The bonus of the first 3 hours" or "The bonus of the first 3 answer" will be given if the score is in the best (top) 3 rewarded score.

Top solvers will be rewarded with daily bonus as usual (65, 60, 55, ... , 10, 5, 0),
but the others will be rewarded with a ratio based on their score.

Also an extra bonus of 75 points will be distributed among the top solvers.

T
he 2nd best solver(s) will receive the half of a share of the 1st best solver(s).

The 3rd best solver(s) will receive the half of a share of the 2nd best solver(s).

For example, let’s assume 3 competitors found the 1st best score,
5 competitors found the 2nd best score and 9 competitors found the 3rd best score;

Three 1st best scorers will receive 75 / 3 = 25 extra points

Five 2nd best scorers will receive 25 / 2 = 13 extra points

Nine 3rd best scorers will receive 13 / 2 = 7 extra points.

If nobody send the answer in the first hour; the first competitior who send the correct answer in second hour gets 35 bonus points and the others get 20 bonus points.

If nobody send the answer in the first two hours; the first competitior who send the correct answer in third hour gets 35,
the second competitor gets 20 and the others get 10 bonus points.

If nobody send the answer in the first three hours; the first competitor who send the correct answer gets 35,
the second competitor gets 20 and the third get 10 bonus points. (No matter the entering time)

If there is only one correct answer in the first three hours, the competitor who send this correct answer gets 35 bonus points,
the first competitor of the other competitors who send correct answer after the first 3 hours gets 20,
the second competitior gets 10 and the others can't get this bonus point, they get only "Day Bonus".