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each step involves subtracting -1, -10, -100, or -1000 only. example st…

Question

each step involves subtracting -1, -10, -100, or -1000 only.
example
start: 5462, step one: -10, middle result: 5452, step two: -1, target: 5451

  1. start: 5462, target: 4452
  2. start: 5462, target: 5352
  3. start: 5462, target: 5361
  4. start: 5462, target: 4362
  5. start: 9310, target: 8309
  6. start: 9310, target: 9209
  7. start: 9310, target: 8210
  8. start: 9310, target: 8300
  9. start: 9310, target: 929
  10. start: 3100, target: 200
  11. start: 3100, target: 29
  12. start: 3100, target: 20
  13. start: 3100, target: 2
  14. start: 3100, target:
  15. start: 100000, target:
  16. start: 100000, target:

start: 100000, target:
start: 100000, target:
start: 100000, target:

Explanation:

Response

Let's solve problem 1 as an example (we can solve others similarly by finding the difference between start and target, then breaking it into two subtractions of -1, -10, -100, or -1000).

Problem 1:

Start = 5462, Target = 4452

Step1: Find the total difference.

Total difference = 5462 - 4452 = 1010. We need to break 1010 into two subtractions (each -1, -10, -100, -1000). Let's first subtract 1000 (since 1000 is a valid step).
Middle Result after Step One: \( 5462 - 1000 = 4462 \)

Step2: Subtract 10 (since 4462 - 10 = 4452, which is the target).

So Step One: -1000, Step Two: -10. Wait, wait, no—wait, target is 4452. Wait, 5462 to 4452: 5462 - 1000 = 4462, then 4462 - 10 = 4452. Yes. Or another way: 5462 - 10 = 5452, then 5452 - 1000 = 4452. Let's check the example: example had -10 then -1. So let's do it as two steps, each -1, -10, -100, -1000.

Alternative approach: Target is 4452. Start is 5462. Let's see the difference in hundreds, tens, ones. 5462 to 4452: thousands place: 5 - 4 = 1 (so subtract 1000), tens place: 6 - 5 = 1 (subtract 10), ones place: 2 - 2 = 0. So total subtract 1000 + 10 = 1010. So Step One: -1000, Middle Result: 5462 - 1000 = 4462; Step Two: -10, Target: 4462 - 10 = 4452.

Step1: Find the difference: 5462 - 5352 = 110. Break into two subtractions. Let's subtract 100 first.

Middle Result: \(5462 - 100 = 5362\)

Step2: Subtract 10 (5362 - 10 = 5352, target).

So Step One: -100, Step Two: -10.

Step1: Difference: 5462 - 5361 = 101. Break into -100 and -1.

Middle Result: \(5462 - 100 = 5362\)

Step2: Subtract 1: \(5362 - 1 = 5361\) (target).

So Step One: -100, Step Two: -1.

Answer:

for Problem 1:
Step One: \(-1000\), Middle Result: \(4462\), Step Two: \(-10\) (or Step One: \(-10\), Middle Result: \(5452\), Step Two: \(-1000\))

Problem 2:

Start = 5462, Target = 5352