A number is formed by writing the numbers 1 to 30 in order as shown.
12345678910111213..........2930
Simeon removed 45 of these 51 digits leaving 6 in their original order to make the largest 6-digit number possible. What is the this number?
n=123456789101112131415161718192021222324252627282930;s=0;p=0;cycle: s=s+(n%10);p=p+1;n=int(n/10);if(n!=0, goto cycle,0);print"Total Sum =",s;print"Total Num =",p
920,212 - is the largest such number.
+1252 We want the earliest digits to be the biggest. Let's start with 9 since that's the biggest number.
9_____
Now, the only numbers left we can use are 10, 11, 12, etc. all the way to 30.
30 is the biggest one, so let's use that next.
930___
BUT WAIT! There are no digits greater than 30. So let's do 29.
929___
Then 30
92930_
Here, we run into a problem. The last digit must be a single digit, but there is no single-digit remaining.
If we choose two one-digit numbers in the beginning, then it will work out.
Obviously, 8 and then 9 is the best option.
89____
Then, since 30 cannot be used after these two numbers, we must use 29 and then 30.
Therefore, 892930 is the answer.
You are very welcome!
:P
