**MENTAL SQUARE ROOTS - This is the category of extracting the square roots of randomly generated numbers with a fixed number of digits, announced before the competition, up to 5th digits after comma.**

Type of the Competition |
of the Questions |
Operations needed for the Answers |
Points for Each Question |
Number of Questions |
Time |
||
---|---|---|---|---|---|---|---|

Number of Digits before Comma |
Number of Digits after Comma |
Total Number of Digits |
|||||

Mental Square Roots (6 Digits) | 6 | 3 | 5 | 8 | 36 | 10 | 15 min. |

Mental Square Roots (8 Digits) | 8 | 4 | 5 | 9 | 45 | 10 | 18 min. |

Mental Square Roots (10 Digits) | 10 | 5 | 5 | 10 | 55 | 10 | 22 min. |

(There can be more than one attempt in this category if time allows.)

**Software:** MEMORIAD™ Competition Software

**Stages of the Competition**

1. 10 random numbers are generated with digits determined beforehand by MEMORIAD™ Competition Software.

2. All the numbers must be consistent with the numbers of the digits determined, that is, the first number cannot be "0".

3. The generated numbers must be the numbers that can be operated up to the 5th digit after comma. The numbers with integer square roots are not generated for the operations.

4. The square roots of the generated numbers must be operated mentally.

5. The operations must be carried out up to the 5th after comma. The 5th digit after comma must be rounded depending on the value of the 6th digit.

For example, the square root of 587247 is 766.32042906..., so when the 6th digit after comma is taken into consideration, the correct answer must be 766.32043.

6. The competitor must enter the results of the operations on the computer. However, he/she cannot write any clue information anywhere.

7. The competitors are free to use the maximum time they are allowed to use. But, if the competitor who finishes the operations in this stage earlier and stops the timer, he cannot see the questions on the screen anymore. Instead, he can check his results on the screen shown by the software. (*)

8. It is important that the timer be stopped as soon as the operations are finished since the winner will be the competitor who finishes operating all the questions correctly in the shortest time.

9. After the competitors finish their operations, they can see their answers and the correct answers on the screen. They can also see their points on the screen.

10. The competitors have 3 minutes to check their answers. When the given time finishes, the software closes the the result page and opens the homepage.

11. The competitor whose result page is closed or who closes the page himself must wait silently for the other competitors to finish their task.

12. Even if there are competitors who have not finished their task yet until the end of the given time, the screen is closed automatically and the result page is opened. (*)

**(*)** Memoriad™ Committee may decide to announce all the results after the end of the operation stage for all competitors.

**Scoring**

1. Each digit of a number has a different value.

2. Beginning from the left, each digit has a point / points up to the 5th digit after comma. For instance, the point of the 1st digit is 1, the point of the 2nd digit is 2, and the point of the 3rd digit is three.

3. Each digit up to up to the 5th digit after comma is checked in the scoring process.

In other words, beginning from the left;

1 point for the 1st digit;

3 (1 + 2) points for the 2nd digit;

6 (1 + 2 + 3) points for the 3rd digit;

10 (1 + 2 + 3 + 4) points for the 4th digit;

15 (1 + 2 + 3 + 4 + 5) points for the 5th digit;

21 (1 + 2 + 3 + 4 + 5 + 6) points for the 6th digit;

28 (1 + 2 + 3 + 4 + 5 + 6 + 7) points for the 7th digit;

The competitors get point / points for the correct answer for each digit up to the 5th digit after comma.

4. The digits are controlled by the Formula |A-B| <= 5*10^(M-N-1).

**The meanings of the parameters in the formula;**

** A : **The answer written by the competitor,

** B : **The correct answer of the question,

** M : **The number of the digits of the correct answer before comma minus 1.

** N : **The number of the digit to be controlled.

To give an example;

The competitor is asked to calculate the square root of 56325487, which is an 8-digit number. His answer is 7505.23568 and the correct answer is 7505.03078.

Now, let’s check the answer for the 4 digit integer part and 5 digit decimal part;

|A-B| <= 5*10^(M-N)

|7505.23568-7505.03078| <= 5*10^((4-1)-9)

|0.2049| <= 5*10^(-6)

The answer is not correct depending on the 9th digit because it is not consistent with 0,2049 <= 0,000005.

Similarly;

The answer is not correct depending on the 8th digit because it is not consistent with 0,2049 <= 0,00005.

The answer is not correct depending on the 7th digit because it is not consistent with 0,2049 <= 0,0005.

The answer is not correct depending on the 6th digit because it is not consistent with 0,2049 <= 0,005.

The answer is not correct depending on the 5th digit because it is not consistent with 0,2049 <= 0,05.

The answer is correct depending on the 4th digit because it is consistent with 0,2049 <= 0,5.

As a result, the competitor gets 1 + 2 + 3 + 4 = 10 points regarding the 4 digits.

5. There can be some exceptional cases;

The explanations below are given by taking the answers of the questions with 6 digits into consideration. If the number of the digits changes, the same process with the same rules are applied.

a-) If the correct answer is greater than 950, the answer cannot be written in 1000 considering for the first two digit round operation, so at least one digit is considered true in the answers beginning with 9xx,xxxxx. For example, if the correct answer is 972.xxxxx and the answer of the competitor is 910.xxxxx, 1 digit is considered true even though no digit (0) is correct depending on the formula above.

b-) Similarly, if the correct answer is greater than 995.xxx, at least two digits are considered true in the answers beginning with 99.

c-) If the correct answer is greater than 999.5xxx, at least three digits are considered true in the answers beginning with 999.

6. Below is a summary of the scoring for different digits of square roots.

The difference between the Correct Answer and the Given Answer |A-B| |
Contol Value (*) 5*10^(M-N) |
The Number of Correct Digits with respect to the equality | |||
---|---|---|---|---|---|

For 6-Digit Questions | For 8-Digit Questions | For 10-Digit Questions | |||

The difference between the Correct Answer and the Given Answer | <= | 5000 | - | - | 1 |

The difference between the Correct Answer and the Given Answer | <= | 500 | - | 1 | 2 |

The difference between the Correct Answer and the Given Answer | <= | 50 | 1 | 2 | 3 |

The difference between the Correct Answer and the Given Answer | <= | 5 | 2 | 3 | 4 |

The difference between the Correct Answer and the Given Answer | <= | 0.5 | 3 | 4 | 5 |

The difference between the Correct Answer and the Given Answer | <= | 0.05 | 4 | 5 | 6 |

The difference between the Correct Answer and the Given Answer | <= | 0.005 | 5 | 6 | 7 |

The difference between the Correct Answer and the Given Answer | <= | 0.0005 | 6 | 7 | 8 |

The difference between the Correct Answer and the Given Answer | <= | 0.00005 | 7 | 8 | 9 |

The difference between the Correct Answer and the Given Answer | <= | 0.000005 | 8 | 9 | 10 |

**(*) Control Value ;** is 5*10^(2-N) for 6-digit numbers, 5*10^(3-N) for 8-digit numbers, and 5*10^(4-N) for 10-digit numbers. **N **stands for the number of the digit to be controlled

7. The points for the answers of the competitor are added for each question as stated above.

8. The raw score is turned into the final score by taking the time the competitor used into consideration, and the process is carried out by the following formula;

**P :** The raw score of the competitor

**t :** The time the competitor used during the task in seconds. ( If the competitor cannot give complete answers for all the questions, the time is considered as **T**.)

**T:** The time given for the task in seconds.

9. The winner is the competitor who gets the highest score.

10. If there are more than one attempts, the highest score that the competitors get in the attempts is considered to be their final score.

11. In case of a tie, the rank is determined by the second best scores of the competitors.