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.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
.xxxxxxxxxx
Find the ten 10-digit decimals.
None of them are the same.
None of their digits are the same.
One of them is the sum of all the others.

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10 answers to this question

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not sure if it's the smallest yet, but it's probably getting pretty close at least:

.0123456789

.0123456798

.0123456879

.0123456897

.0123456978

.0123456987

.0123457689

.0142675398

.0196582374

.1203456789

I'm thinking this HAS to be the smallest possible sum...here's why:

The smallest valid number we can use is .0123456789

So if we do that 9 times (illegally, of course...but just doing it for the sake of demonstration), the sum would be .1111111101...which would be the absolute minimum value for the 10th number.

Obviously that isn't a valid number (according to the constraints of the problem), so the closest number we can get to that absolute minimum would be .1203456789

Which is the answer I have above.

Now, I there are multiple WAYS to get that sum, but it should be the minimum sum.

Edited by Pickett

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Questions:

1)"None of their digits are the same." - does this mean none of the digits in the same decimal place are the same for the different numbers or none of the digits in the same number are the same or both?

2)The location of the decimal point is variable rather than at the location shown, i.e. at the beginning of the number?

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Questions:Answer

1)"None of their digits are the same." - does this mean none of the digits in the same decimal place are the same for the different numbers or none of the digits in the same number are the same or both?

: None of the digits in the same number are the same. (OP)

2)The location of the decimal point is variable rather than at the location shown, i.e. at the beginning of the number?

: The location of the decimal point is at the beginning of the number.(OP)

Note: ignore 0 before decimal point

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The first starts with .0; the next eight with .1; the 10th with .9.

Thus,

.0xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.1xxxxxxxxx
.9xxxxxxxxx
The second digits must be small in the first nine numbers, as well -- no more than 1 can be carried.
Ah, no. More than one of them must start with .0.
Going somewhere to scratch my head.

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.0123456789


.0123456798
.0123456879
.0123456897
.0123456978
.0123456987
.0123457689
.0123457698
.0247138965
.1234795680
  • Upvote 1

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not sure if it's the smallest yet, but it's probably getting pretty close at least:



.0123456789
.0123456798
.0123456879
.0123456897
.0123456978
.0123456987
.0123457689
.0142675398
.0196582374
.1203456789
Edited by Pickett

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.1097386542


.1097386524
.1097386452
.1097386425
.1097386254
.1097386245
.1097385624
.1097384562
.1097364582
.9876453210

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