Biggest Number

Probability Level 4

$N$ is a number where integers from 1 through 60 are written continuously, thus $N=1234567891011...585960.$ What is the largest possible number that could be made after 100 digits are removed?

Note: You are not allowed to rearrange the digits that remain. For instance if we remove the last 100 digits, then we can only have the number 12345678910.

The answer is 99999785960.

4 solutions

Aditya Raut
Jul 31, 2014

We have six 9s available. After removing 100 digits, we remain with 11 digits.

Out of the six 9s, we can get five at start of the number. (if all 6 are at start, we can't get an 11-digit number)

Thus after taking the first five 9s, which are taken from 9,19,29,39 and 49, we are wanting to form the largest 6 digit number from removing digits of $5051525354555657585960$ and clearly even by observation that will be $785960$ .

So the number we want is $\boxed{99999785960}$

But there are six number 9 and six number 8 :/ So from 1->60 we have 111 digits and we will remove 100 digits therefore 11 digits will remain and 99999988888 is the largest

Raymond John Diaz - 6 years, 10 months ago

They are not in the same order my friend. We can't take them , because the $8$ in $18$ and $28$ are before $9$ in $39$ and $49$ and $59$ . So you can't directly take that, the numbers are formed by removing digits not directly arranging the biggest ones.

Aditya Raut - 6 years, 10 months ago

My answer is also 99999988888

Rupesh Kumar - 6 years, 10 months ago

Aditya Raut - 6 years, 10 months ago

Figel Ilham
Aug 1, 2014

Rewrite 123456789....5859560

Since there are digits 9, the largest possible number for the most left place is 9, so we delete 12345678 Now, we have to remove 92 digits

Write: 9101112131415...585960

Delete also 1011121314151617181 We don't delete 9 since we must try to make largest

There are 19 digits from 1011121314151617181, so we hae to delete 92-19=73 digits left

Write: 99202122...585960

We delete also 2021222324252627282, 3031323334353637383 and 4041424344454647484

it means that we have removed 19(3) = 57 digits Then, we need to remove 73-57=16 digits Since 16<19, we have to use a little logic here

Write 999995051525354555657585960 We must absolutely delete 505152535455 since those number aren't necessary to fit the new one - it means that we have removed 12 digits 4 remains left

Rewrite 999995657585960

We have to delete 565 and digit 5 between 7 and 8 since 6<7 Now, we have deleted 100 digits

Thus, we get 99999785960

Jaiveer Shekhawat
Aug 20, 2014

These who had given their solutions down, had done the only and only solution. so, it's meaningless to jot it down again.

Timothy Wong
Apr 26, 2014

(9)1(9)2(9)3(9)4(9)(585960)=(99999585960)

I think that 99999785960 is larger ad solvable too.

Aloysius Ng - 7 years ago

I have updated the answer to 99999785960

In future, if you spot any errors with a problem, you can “report” it by selecting the “dot dot dot” menu in the lower right corner. You will get a more timely response that way.

Calvin Lin Staff - 6 years, 10 months ago

can't 99999988888 be the answer , as there will be 11 digits left after removing 100 digits and for getting largest value we should place all the six 9's available with us at the beginning followed by 8's . plz explain what mistake i am doing.

akash deep - 6 years, 10 months ago

@Akash Deep – I also think so @Akash Deep. Will someone explain why it's wrong?

Sagnik Saha - 6 years, 10 months ago

@Akash Deep – You can't change the order of the digits after removing the 100 digits

C D - 6 years, 10 months ago

@C D – but this wasn't mentioned in the question

akash deep - 6 years, 10 months ago

it was so simple but i thought that we have to arrange these nos. after removing the digits.

prashant goyal - 6 years, 10 months ago

Biggest Number

The answer is 99999785960.

4 solutions

0 pending reports