REMOVING NUMBERS

	1	2	3	4	5	6	7	8	9
A	9	6	5	3	1	3	6	4	7
B	4	7	4	8	1	8	5	9	5
C	2	4	3	1	2	3	8	2	8
D	7	9	6	9	6	7	4	1	3
E	1	9	2	4	7	5	1	5	2
F	6	1	7	2	2	8	3	1	4
G	9	6	5	8	9	7	6	4	7
H	5	9	4	3	7	1	5	9	5
I	8	2	3	6	3	6	8	2	8

81 numbers which contain 9 x each number are placed into the above platform.
Move to any cell, and remove from the platform the moved cell and the maximum 4 of the diagonal cells which have the same distance to the moved cell.
For instance, if you moved to the B2, as in the first example you can remove the 5 cells or as in the second & third examples you can remove 2 cells.

If you move to B3 you can remove 5 or 3 cells.
 

 

However, you have to remove the maximum cells which include numbers in them.

In the first option (5 cells) if there are 5 or 4 cells including numbers in them then you have to remove them,
but if there are 3 cells including numbers in first option and the second option also have 3 cells including numbers then you can make choice between them.
Namely, if one option has maximum cells in which they include numbers then you have to choose that option.

If you had moved to C3 then you can choose whether taking the 5 cells in first option or the 5 cells in the second option.

 

However, you have to take the one which has much numbers.

With a single movement you can remove min 2 max 5 numbers.
You can not remove a single cell which does not have any number at its diagonals.
That cell remains in the platform (look at to the example solutions)

For example: If you make the D4 movement in the position below; you have to remove 5, 3 and 4.
In this situation 2 remains in the platform.
If you want to remove 5 and 3 then you have to make C5 movement.
In this case, you can remove the 2 and 4 (which can be in each other’s diagonal) with the next movement.

Each remaining number in the platform will have negative effect on your score!

Make the movements and remove the group of numbers in each with obeying these rules. In each movement create a number using the numbers that you removed and write them one after the other according to your movement sequence in right aligned format.

 

Rules:

 1) All numbers should be right aligned.

 

 2) For each number except the first and the last number; if the previous number is smaller than its own then the next one also should be smaller and if the previous number is bigger than its own then the next one also should be bigger. Which means; numbers should be in order one big – one small.

 

 3) In the list, digits of numbers can not be same with the previous or next one’s same order digit

 

 4) In the list same number can not be used more than once.

 

INVALID LISTINGS					VALID LISTINGS
53422	53422	53422	53422		53422
3254	2341	3254	4215		4215
43125	1235	41355	51423		51423
423	34521	531	4215		4214
RULE 1	RULE 2	RULE 3	RULE 4

 

 

 

 

 

 

 

 

 

If you could generate a list by obeying the rules: Find each numbers’ grade value.

GRADE VALUE : Firstly, multiply the number of different digit counts with the total digit count. Then, multiply this result with the number.

 

54321 x 5	=	271605	42444 x 4 x 5	=	84880
55321 x 2 x 5	=	553210	2322 x 3 x 4	=	27864
55323 x 2 x 2 x 5	=	1106460	534 x 3	=	1602
54545 x 3 x 2 x 5	=	1636350	33 x 2 x 2	=	132

 

 

 

 

 

If there is not any number remaining in the platform then your total score is the sum of your all grades.

If there are remaining numbers in the platform then firstly find the sum of your all grades and for each number remained; subtract the first grade which starts with that number from your total score.

If a number starting with that number does not exist in your list then search for the first number which the second digit is your remaining number (if still does not exist, then search for third digit, then fourth, then fifth, …)

Examine the example solutions and the score calculations carefully.

EXAMPLE PUZZLE – EXAMPLE SOLUTION 1: