## Task 11/62

Calculation of the year 1962 from the birthday

Write down your birthday. Double the number of the day and add the number of the month to the result.

(Example: Birthday 27.8., number of the day 27, number of the month 8, calculation: 2 * 27 + 8 = 62.) Multiply this new result by 5 and add 400. Subtract the tenfold of the day number from this. From the double of this result, subtract the tenfold of the month number.

If you multiply the number thus obtained by 2.5 and finally subtract 38, you get the number 1962. How is this possible with such different initial values?
If we denote the day number as $a$ and the month number as $b$, the following calculation follows from the instructions in the problem:

1) Doubling the day number: $2 a$
2) Adding the month number: $2 a + b$
3) Multiplying by 5: $5 \cdot (2 a + b) = 10 a + 5 b$
4) Adding 400: $10 a + 5 b + 400$
5) Subtracting the tenfold of the day number: $10 a + 5 b + 400 - 10 a = 5 b + 400$

We can see that part of the date "falls out" of the calculation.

6) Doubling the result: $10 b + 800$
7) Subtracting the tenfold of the month number: $10 b + 800 - 10 b = 800$

Now the rest of the date has "fallen out." For all possible initial values, the same intermediate result is now present.

8) Multiplying by 2.5: $2.5 \cdot 800 = 2000$
9) Subtracting 38: $2000 - 38 = 1962$