Katie and Charlotte had \(4\) sheets of paper. They cut some of the sheets into \(4\) pieces. They then cut some of the newly obtained papersheets also into \(4\) pieces. They did this several more times, cutting a piece of paper into \(4\). In the end they counted the number of sheets. Could this number be \(2024\)?
By checking which of the following numbers are divisible by \(11\): \[121,\,143,\,286,\,235,\,473,\,798,\,693,\,576,\,748\] can you find and prove a condition that is enough to guarantee a number is divisible by \(11\)?