Eating the tasty numbers!

Computer Science Level 3

Given a natural number, we start \(\color{Blue}{\text{eating the number}}\) from either left or right i.e. we start removing its digits one by one from left to right, or from right to left.

We define a set \(\color{Blue}{\text{dish}}\) of the number, which is obtained by noting the number formed after eating every digit (The original number is also included) .

The \(\color{Blue}{\text{taste}}\) of a number is sum of all numbers in that number's dish.

What is the smallest non-palindromic number which when eaten from left gives same taste as eating from right?

Details and Assumptions:

  • The dish of a number can be obtained in 2 ways, either eating from left or eating from right and hence there'll be 2 tastes for each number (maybe the same, that's where you count the number!)

  • Example of a dish, dish of the number 12635 as eaten from left will be \(\{12635,2635,635,35,5\}\) and its dish when eaten from right will be \(\{12635,1263,126,12,1\}\)

  • Taste of the number 123 will be \(123+23+3 = 149\) from left and it will be \(123+12+1 = 146\) from right.

  • A non-palindromic number is the one which is not the same when read from left or from right, e.g. \(12321 , 22 , 1441, 8\) are some examples of palindromic numbers, whereas \(98,234,239478 \) are some non-palindromic numbers.


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