# How to devise this solution to Non-Constructible Change challenge from Algoexpert.io

I'm working through algoexpert.io coding challenges and I'm having trouble undersatnding the suggested solution to one of the questions titled Non-Constructible Change

Here's the challenge question:

Given an array of positive integers representing the values of coins in your possession, write a function that returns the minimum amount of change (the minimum sum of money) that you cannot create. The given coins can have any positive integer value and aren't necessarily unique (i.e., you can have multiple coins of the same value).

For example, if you're given coins = [1, 2, 5], the minimum amount of change that you can't create is 4. If you're given no coins, the minimum amount of change that you can't create is 1.

``````// O(nlogn) time, O(n) size.
function nonConstructibleChange(coins) {
coins = coins.sort((a, b) => a - b); // O(nlogn) time operation
let change = 0;

for (coin of coins) {
if (coin > change + 1) return change + 1;
change += coin;
}

return change + 1;
}
``````

My problem

I am not completely sure how did the author of the solution come up with the intuition that

``````if the current coin is greater than `change + 1`, the smallest impossible change is equal to `change + 1`.
``````

I can see how it tracks, and indeed the algorithm passes all tests, but I'd like to know more about a process I could use to devise this rule.

Thank you for taking the time to read the question!