TurkZeka 2007/1 Puzzle Competition


Puzzle 7: The Calculation Optimization

124  216  315  412  784  936  1248

The numbers above have two common properties.
First, find these two common properties, then with the numbers which have minimum 2 digits and same properties, make a mathematical calculation; so that the number which is the result of the calculation will have the same properties. (You can also use the numbers at the top.)

THE RULES:
You cannot use the same number more than once in the calculation.
You have to use each of the signs "x", "/", "+" and "-" at least once in the calculation.
But, you cannot use none of these signs more than four times.
The order of the calculations must be from left to right like calculator. (Not mathematical ordinary)
None of the signs has priority. (Look at the example solution.)
You cannot use the paranthesis.
There cannot be "0" (zero) in the digits.
Attention ! Of course, that "There cannot be zero" rule is not one of the common properties. But, this rule can be a clue for you to find the common properties of the numbers.

ATTENTION !
The numbers like 527, 812, 3951, 3135, 2412 are invalid numbers for this puzzle since they have only one of the common properties.

Find your score by multiplying the result of your score with the total digit count (not including the result) of your calculation. (Look at the example solution.)

A valid example solution: 312x36/432+264–128=162
Score: 162x14=2268
(Your score doesn't need have this properties.)

Answering Format: Don't use space. First, enter your score, then enter the sign ":" and then enter all calculation.
The answer for the example: 2268:312x36/432+264-128=162

POINTS:
The owner(s) of the best score will be rewarded with 200 points, and others who manage
to find more than 3/5 of the best score will be rewarded according to the
ratio based on the best. (If the best score is 100, 61 will be required in order to be rewarded)
The solutions of the competitors whose scores are less than the rewarding limit will not be 
checked.

The bonus of the first 3-hours will be given if the score is in 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.

The 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