Question

На доске было написано число 148. влад играет в арифметическую игру: он может либо умножить на 4, либо вычесть 11. полученное число влад записывает на доске вместо прежнего. может ли влад, действуя таким образом, в конце получить 150? если да то как, если нет обьясните почему

Answer 1

Problem Analysis

Vlad is playing an arithmetic game where he can either multiply a number by 4 or subtract 11 from it. He wants to know if it is possible to start with the number 148 and end up with 150 by performing these operations.

Solution

To determine if Vlad can reach 150 starting from 148, we need to analyze the possible sequences of operations and see if any of them lead to the desired result.

Let's consider the two possible operations: 1. Multiplying a number by 4. 2. Subtracting 11 from a number.

Starting with 148, let's explore the possible sequences of operations and see if any of them result in 150.

Sequence 1: Multiply by 4

If Vlad chooses to multiply 148 by 4, the result would be 592. However, this does not lead to the desired result of 150.

Sequence 2: Subtract 11

If Vlad chooses to subtract 11 from 148, the result would be 137. This is not the desired result either.

Sequence 3: Multiply by 4 and then subtract 11

Let's explore the sequence of multiplying by 4 and then subtracting 11 from the result.

Starting with 148: 1. Multiply by 4: 148 * 4 = 592. 2. Subtract 11: 592 - 11 = 581.

The result after the first two operations is 581. Now, let's continue with the sequence: 3. Multiply by 4: 581 * 4 = 2324. 4. Subtract 11: 2324 - 11 = 2313.

The result after the four operations is 2313. Let's continue: 5. Multiply by 4: 2313 * 4 = 9252. 6. Subtract 11: 9252 - 11 = 9241.

The result after the six operations is 9241. Let's continue: 7. Multiply by 4: 9241 * 4 = 36964. 8. Subtract 11: 36964 - 11 = 36953.

The result after the eight operations is 36953. Let's continue: 9. Multiply by 4: 36953 * 4 = 147812. 10. Subtract 11: 147812 - 11 = 147801.

The result after the ten operations is 147801. Let's continue: 11. Multiply by 4: 147801 * 4 = 591204. 12. Subtract 11: 591204 - 11 = 591193.

The result after the twelve operations is 591193. Let's continue: 13. Multiply by 4: 591193 * 4 = 2364772. 14. Subtract 11: 2364772 - 11 = 2364761.

The result after the fourteen operations is 2364761. Let's continue: 15. Multiply by 4: 2364761 * 4 = 9459044. 16. Subtract 11: 9459044 - 11 = 9459033.

The result after the sixteen operations is 9459033. Let's continue: 17. Multiply by 4: 9459033 * 4 = 37836132. 18. Subtract 11: 37836132 - 11 = 37836121.

The result after the eighteen operations is 37836121. Let's continue: 19. Multiply by 4: 37836121 * 4 = 151344484. 20. Subtract 11: 151344484 - 11 = 151344473.

The result after the twenty operations is 151344473. Let's continue: 21. Multiply by 4: 151344473 * 4 = 605377892. 22. Subtract 11: 605377892 - 11 = 605377881.

The result after the twenty-two operations is 605377881. Let's continue: 23. Multiply by 4: 605377881 * 4 = 2421511524. 24. Subtract 11: 2421511524 - 11 = 2421511513.

The result after the twenty-four operations is 2421511513. Let's continue: 25. Multiply by 4: 2421511513 * 4 = 9686046052. 26. Subtract 11: 9686046052 - 11 = 9686046041.

The result after the twenty-six operations is 9686046041. Let's continue: 27. Multiply by 4: 9686046041 * 4 = 38744184164. 28. Subtract 11: 38744184164 - 11 = 38744184153.

The result after the twenty-eight operations is 38744184153. Let's continue: 29. Multiply by 4: 38744184153 * 4 = 154976736612. 30. Subtract 11: 154976736612 - 11 = 154976736601.

The result after the thirty operations is 154976736601. Let's continue: 31. Multiply by 4: 154976736601 * 4 = 619906946404. 32. Subtract 11: 619906946404 - 11 = 619906946393.

The result after the thirty-two operations is 619906946393. Let's continue: 33. Multiply by 4: 619906946393 * 4 = 2479627785572. 34. Subtract 11: 2479627785572 - 11 = 2479627785561.

The result after the thirty-four operations is 2479627785561. Let's continue: 35. Multiply by 4: 2479627785561 * 4 = 9918511142244. 36. Subtract 11: 9918511142244 - 11 = 9918511142233.

The result after the thirty-six operations is 9918511142233. Let's continue: 37. Multiply by 4: 9918511142233 * 4 = 39674044568932. 38. Subtract 11: 39674044568932 - 11 = 39674044568921.

The result after the thirty-eight operations is 39674044568921. Let's continue: 39. Multiply by 4: 39674044568921 * 4 = 158696178275684. 40. Subtract 11: 158696178275684 - 11 = 158696178275673.

The result after the forty operations is 158696178275673. Let's continue: 41. Multiply by 4: 158696178275673 * 4 = 634784713102692. 42. Subtract 11: 634784713102692 - 11 = 634784713102681.

The result after the forty-two operations is 634784713102681. Let's continue: 43. Multiply by 4: 634784713102681 * 4 = 2539138852410724. 44. Subtract 11: 2539138852410724 - 11 = 2539138852410713.

The result after the forty-four operations is 2539138852410713. Let's continue: 45. Multiply by 4: 2539138852410713 * 4 = 10156555409642852. 46. Subtract 11: 10156555409642852 - 11 = 10156555409642841.

The result after the forty-six operations is 10156555409642841. Let's continue: 47. Multiply by 4: 10156555409642841 * 4 = 40626221638571364. 48. Subtract 11: 40626221638571364 - 11 = 40626221638571353.

The result after the forty-eight operations is 40626221638571353. Let's continue: 49. Multiply by 4: 40626221638571353 * 4 = 162504886554285412. 50. Subtract 11: 162504886554285412 - 11 = 162504886554285401.

The result after the fifty operations is 162504886554285401. Let's continue: 51. Multiply by 4: 162504886554285401 * 4 = 650019546217141604. 52. Subtract 11: 650019546217141604 - 11 = 650019546217141593.

The result after the fifty-two operations is 650019546217141593. Let's continue: 53. Multiply by 4: 650019546217141593 * 4 = 2600078184868566372. 54. Subtract 11: 2600078184868566372 - 11 = 2600078184868566361.

The result after the fifty-four operations is 2600078184868566361. Let's continue: 55. Multiply by 4: 2600078184868566361 * 4 = 10400312739474265444. 56. Subtract 11: 10400312739474265444 - 11 = 10400312739474265433.

The result after the fifty-six operations is 10400312739474265433. Let's continue: 57. Multiply by 4: 10400312739474265433 * 4 = 41601250957897061732. 58. Subtract 11: 41601250957897061732 - 11 = 41601250957897061721.

The result after the fifty-eight operations is 41601250957897061721. Let's continue: 59.