Find the total number of subtraction remaining 1111?

[Helly123]

Homework Statement

Homework Equations

The Attempt at a Solution

5 digits minus 4 digit remaining 11111?
if the 5 digit = 20000
and the 4 digit = 8889
so remaining 11111

digits 1 to 9 have been used?
what am I supposed to do?

 

[SammyS]

Homework Statement

View attachment 206408

Homework Equations

The Attempt at a Solution

5 digits minus 4 digit remaining 11111?
if the 5 digit = 20000
and the 4 digit = 8889
so remaining 11111

digits 1 to 9 have been used?
what am I supposed to do?

Wow. The wording of this problem had me stumped. I had to read it many times before maybe figuring out what it's asking.

I think it must mean:

Suppose A and B have 5 and 4 digits respectively, and that A − B = 11111 . Furthermore, all digits 1 - 9 are used in writing the combination of A and B.
What are all of the possible sets of numbers A and B for which this is true?​

.

 

[Helly123]

Wow. The wording of this problem had me stumped. I had to read it many times before maybe figuring out what it's asking.

I think it must mean:

Suppose A and B have 5 and 4 digits respectively, and that A − B = 11111 . Furthermore, all digits 1 - 9 are used in writing the combination of A and B.
What are all of the possible sets of numbers A and B for which this is true?​

.

I get 19753 - 8642 = 11111. But i don't know, total number of substractions? 8+6+4+2 = 20... the key answer different

 

[SammyS]

I get 19753 - 8642 = 11111. But i don't know, total number of subtractions? 8+6+4+2 = 20... the key answer different

As long as each pair, {9, 8}, {7, 6}, {5, 4}, {3, 2} is lined up together, you will have the correct result.

Can you show that the leading digit in the 5 digit number can't be a 2 ?

 

[Helly123]

As long as each pair, {9, 8}, {7, 6}, {5, 4}, {3, 2} is lined up together, you will have the correct result.

Can you show that the leading digit in the 5 digit number can't be a 2 ?

The leading number can't be 2, because that leading number won't be substracted , thus is 1. ?

 

[mfb]

How do we get a "number of subtractions" that way?

The way I interpreted it, we start with a 5-digit number, let's say 35791, and then subtract a 4-digit number, let's say 2468, repeatedly until the result is 11111:
35791-n*2468= 11111
This has n=10 as solution.

With that interpretation we don't get a unique solution, on the other hand, as we have n=10 and n=1 as examples already.

The leading number can't be 2, because that leading number won't be substracted , thus is 1. ?

It is a bit more complicated as the 4-digit number could start with 9.

Do you know the intended answer?

 

[Kaura]

Poorly worded questions honestly but I think that mfb's interpretation is probably correct