One of the simplest and most effective exercises for training memory at any age is mental counting. You can come up with many different options for training mental counting, but here a very important point is the interest in these exercises and the result of calculations.
We offer for training an exercise in calculating the day of the week for a specific date.
On the one hand, it can be useful in a specific situation to quickly determine on which day of the week you or your friends were born, or on which day of the week your previous birthday was or will be your next birthday. Or maybe surprise your interlocutor a little by telling him that he was born on a particular day of the week.
On the other hand, this is not a simple exercise of only addition or subtraction. Here it will be necessary in the mind, and divide, and add, and substitute certain numbers instead of the values of the month. Let's move on to the algorithm of such a calculation.
CALCULATION OF THE DAY OF THE WEEK FROM A DATE
Consider first the four main parameters for calculations.
Let's take the date - 11/20/1957
The annual index is calculated in such a way that the last two digits of the year are divisible by 12. For example, the number 57 is taken from the year 1957. This number is divided by 12, and the remainder is 4 and 9.
The remainder is divisible by 4. In our example, the remainder is 9, which when divided by 4 gives 2 and a remainder of 1, but here the remainder is not taken into account.
The three resulting numbers are added together. So 4 plus 9 plus 2 makes 15.
Each month is assigned its own index, which you just need to remember.
Month | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 |
———————————————————————————-
Index | 6 | 2 | 2 | 5 | 0 | 3 | 5 | 1 | 4 | 6 | 2 | 4 |
For years beginning with "one thousand nine hundred ..." + 1 is added
For years beginning with "two thousand..." nothing is added
There is also an additional rule for leap years, which can be recognized by the fact that the last two digits of the year are divisible by 4 without a remainder.
If the original date is January or February leap year, then from the final number it is necessary to subtract - 1
Let's look at a few specific examples.
1. Calculate the day of the week for the date 11/20/1957
Let's add up all the indices:
Index of the year — 15 (4+9+2)
Month index - 2
Just a date - 20
Century index - 1
So 15 plus 2 plus 20 plus 1 makes 38.
The result is divisible by 7, in our case 38 divided by 7 equals 5 and 3 in the remainder.
The week starts on Monday, which is number 1, and number 3 is Wednesday.
Total: 11/20/1957 is Wednesday.
2. Calculate the day of the week for the date 02/10/1928
Let's add up all the indices:
Index of the year – 7 (2+4+1)
Month index - 2
Just a date - 10
Leap year index - (-1)
Century index - 1
So 7 plus 2 plus 10 plus 1 minus 1 is 19.
The week starts on Monday, which is the number 1, and the number 5 corresponds to Friday.
Total: 02/10/1928 is Friday.
3. Calculate the day of the week for the date 06/15/2012
Let's add up all the indices:
Year index - 1
Month index - 3
Just a date - 15
Century index - 0
So 15 plus 3 plus 1 makes 19.
The result is divisible by 7, in our case 19 divided by 7 equals 2 and 5 in the remainder.
- tutorial
There are many ways to pump the brain. N-back tasks or mobile apps to practice fast mental counting. But these tasks are divorced from the current reality, but I would like to pump the brain with a practical skill.
For what? After all, you can quickly calculate on the gadget. Alas, not at all fast, because. it will take time to search for and activate the gadget, search for the application, enter the date, and understand the result. And you can also please your friends / girlfriends with your suddenly appeared extraordinary abilities. By the way, friends will quickly realize the convenience of using a perpetual calendar with a voice interface.
Is it possible? Once upon a time, we managed without computers. One of the "talent-hunting" TV shows showed a trained three-year-old who can calculate the product of three-digit numbers (save your kids). However, adults are no longer children and their brains are partially crystallized, in the sense that we are poorly trained. So you need to memorize as little as possible and use the available skills as much as possible.
In algorithmics, often the amount of computation can be compensated by the amount of memory. Those. the more RAM available, the less computation required. The brain works similarly - the more we remember, the faster we look for a solution. We remembered a few formulas for solving the Rubik's Cube - you will collect it in a couple of minutes (after a long workout). Remembered one and a half hundred formulas - you will collect them in a couple of tens of seconds. World record 2013 - 8.18 sec. Once again: the more we remember, the faster the solution.
Algorithm
You need to take the offset (day of the week) of the first day of the year (y) and the offset of the month (m). Then calculate the sum y + m + d, where d is the day of the month, and find the remainder after dividing by 7. We get the number of the day of the week.What to remember
Reflections
In general, it is enough to remember all the days of the week for all 28 years (the periodicity is proportional to the product of the periods of leap years and the days of the week). Sequence in 10k. That's quite a lot.
If you add one addition operation, then it will be enough to remember only a couple of rows of numbers:
M(month) = ( 6 2 2 5 0 3 5 1 4 6 2 4 ), from January to December
Y(year) = ( 6 0 1 2 4 5 6 0 2 3 4 5 0 1 2 3 5 6 0 1 3 4 5 6 1 2 3 4 ), from 1988 to 2015
The offsets for the month are taken from the calendar of some year. The month offset is equal to the number of gray squares at the beginning of the month. For example, the non-leap year 2006. The offset for this year will be 0.
Still, remembering the offsets for all the years and then doing a quick index lookup is quite a cognitive task. There is an alternative way - to calculate. You need to take the last two digits of the year (+100 for the XXI century) - Y. Next, find the nearest past leap year Yv. Take dY \u003d Y - Yv. Then the year offset can be calculated
Y(Y) = (50 – Yv/2 + dY)
The disadvantage of the formula is that for 2004 and later the offset will be negative, and for the beginning and middle of the 20th century it will be two-digit, which slightly complicates mental calculations. It is possible to use different formulas for each century, which take into account only the two lower digits of the year. For example, 12 for 2012 and 1912.
XX: (50 - Yv/2 + dY) % 7 or (8 - Yv/2% 7 + dY)
XXI: (7 - Yv / 2% 7 + dY)
As a result, it may be easier to remember the offset table in this form:
The offset for a year can be calculated as the sum of the offset of the next smaller leap year and its difference from the desired year. Seven digits are easier to remember than 28. In addition, the numbers are in descending order with a step of 2. (Yes, yes, (0 - 2) will be 5, remember the remainder of division by 7). You can remember the numbers (6, 4, 2, 0, -2, -4, -6), which will give a similar result when calculating. Years divisible by 20 are located in an oblique 3x3 square according to the "knight's move" scheme with the year 2000 in the center. The values of the offsets of months and years are coordinated so that the offset of 0 falls on the year 2000. And the step between adjacent rows is 28 years.
For example, for 2014 the offset will be y(2014) = y(2012) + 2 = 1 + 2 = 3. And the day of the programmer on September 13, 2014 will be (y(2014) + m(Sep) + 13) = (3 + 4 + 13) = 20 => 20% 7 = 6, i.e. Saturday.
We structure a series of offsets for months. It is convenient to memorize the values according to the seasons: spring, summer, autumn, winter.
Notice that suddenly (?), in order from top to bottom and left to right, the numbers lined up in an ascending row (first color table). You can remember only the remainders of division by 7 (second color table) or to restore the entire table, remember only the differences (last table). Adding 1 to 1, we get 2 for March, 2+1=3 for June, 3+1=4 for September, and so on. Identical values are painted in the same colors. For a quick search, the second color table will help us. Remember that the lines are the seasons, starting with spring. This is extremely unusual. But in ancient Rome, the year began with March. This is reflected in the names of the months in Latin numerals: September ber/ Octo ber/ Novem ber/ Decem ber - 7/8/9/10, i.e. February was the last 12th month of the year to which a leap day was added.
Important!!! Programmers have an eternal problem with the lost unit. In our problem, this was not possible without it. For January and February of a leap year, subtract one.
February 14, 2012 = (y(2012)+m(Feb)+14) - 1 = (1 + 2 +14) - 1 => 16% 7 = 2, i.e. Tuesday.
You also need to remember that not all years that are divisible by 4 will be leap years (exceptions are 2100, 1900, 1800, ....). Accordingly, it is necessary to take into account the offset for the eyelid. However, even if you do not take into account the last exception, you can accurately operate with the days of the week for the 20th and 21st centuries, which is sufficient for most everyday cases.
A bit of optimization.
Calculations can be performed in streaming mode. Usually, the date of birth (or any other date) is reported starting from the day of the month, for example, December 23, 1913. Those. in the process of reporting the date, you can partially calculate the desired sum 23 + m(Dec) = 27 or even 23% 7 + m(Dec) = 2 + 4 = 6 and then think y(1913) = y(1912) + 1 = 3. As a result, report 30% 7 = (6 + 3) % 7 = 2, Tuesday.Often you have to operate with the dates of the current year. Those. you will always remember the offset of the year, because from frequent use, the value will be cached. For example, for 2014 the offset is 3.
What we got. The rules for filling out the tables are simple and you most likely remember them and can reproduce the cheat sheet for yourself anywhere at any time. But for quick counting, tables are easier to memorize in their entirety. After all, we do not restore the addition and multiplication tables for calculating change in front of the cash register. These tables are "stitched" in elementary school. The easiest way to memorize tables is to use the Week Brain Calc simulator (Windows Phone).
After a short workout, you can please your loved ones with your unique abilities.
Scientists correlate the days of the week with the planets of the solar system, thereby characterizing each day in terms of magic. Therefore, a person born on a certain day also has his own character, temperament and vocation. So, in order to determine what character traits and capabilities each of us is endowed with, you need to calculate what day of the week was on your birthday and what its meaning is. Using the free online calculation, you can find out how this day affects the character, fate and magical abilities.
What day of the week was your birthday? Calculate online for free:
You can find out for yourself what day of the week was on any day, and read the description below:
Monday.
This day passes under the sign of the Moon, so Monday people have such character traits as indecision and nervousness, they are contradictory by nature, so they often cannot achieve the desired heights. Protective and emotional. They have a rich imagination. Many of them are lonely in life, because they are not ready to take responsibility for someone. As for love relationships, they are true and sincere.
Magic abilities. On the full moon, they can make a wish by standing in front of an open window. It will definitely come true.
Tuesday.
This day is ruled by Mars - a warlike planet. People born on this day are stubborn, assertive and often aggressive. Although they often doubt the correctness of their actions and words. Tuesday people need someone who can lend their strong shoulder in difficult times, it can be a meek and gentle person, so it’s better to choose a soul mate from unobtrusive guys or girls, then the union will be long and happy.
Magic abilities. See prophetic dreams on demand. To do this, you need to lie down before midnight and ask for a dream prediction. You can't get out of bed until morning.
Wednesday.
Mercury rules this day, so people born on Wednesday will constantly engage in self-improvement. They are conservatives, it is hard for them to start something new. Purposeful, from an early age clearly go to the goal. But as soon as what has been achieved is obtained, they begin to get bored and then they give vent to the negative that has accumulated all the time. Then they set a goal again and clearly go to it. In marriage, by the way, they also sometimes need to leave their soulmate for a quiet and secluded place, from where they will return calm and spiritual, then the relationship will be strong and stable.
Magic abilities. They treat headaches with their energy and soothe the nervous system with the laying on of palms.
Thursday.
The leadership on this day is transferred to Jupiter, which means that the people of Thursday are excellent organizers and managers. They are leaders in life, which is why weaker people are drawn to them. Among them are many who are stubborn and intractable, these qualities reach the point of absurdity. At home, they are despots, so an ideal marriage is possible with the driven and the weak. They are owners, so they do not forgive betrayal.
Magic abilities. Intuition is well developed, so they can predict the future.
Friday.
Venus is the patroness of this day of the week, so people born on Friday are optimistic and cheerful, they are flirtatious and even somewhat frivolous. Their house is always warm and cozy, they have many friends and acquaintances. However, it is difficult for them to find a soul mate, since Friday people cannot live within four walls - they need freedom, which not every lover will like, so it is better for jealous people to immediately refuse marriage to Friday persons.
Magic abilities. The scent for profit is well developed, so these people never live in poverty. They always have money and a stable income.
Saturday.
Those born on Saturday are ruled by Saturn, so they can endure a lot. These people are hardworking and smart, they are leisurely, but thorough. They do not like to lead, therefore they do not strive for career growth, they are closer to home comfort. But in the family they are often unhappy, because they believe that marriage is forever, which means that there is no need to take the initiative in maintaining the fire of feelings. Prudence is valued in partners, the rest simply become outcasts for them. Often they are unhappy in their youth and content with life in their mature years.
Magic abilities. Never wrong about a person, their first impression of someone is always right.
Sunday.
People born on Sunday are patronized by the Sun, so they are always comfortable in life. They are active and quite successful, although they cannot be called minions of fate, since quite often serious problems occur with them. The reason for them is the carelessness of Sunday people - they are lazy and optional. There are few family members among them, because they are too lazy to start a family in order to take care of someone. They usually go with the flow, which often brings them to the right and profitable place. These people need to learn hard work and assertiveness. A close person with such traits as prudence and authority helps them achieve a lot in life.
Magic abilities. Luck and the ability to guess lottery numbers, which they often use.
