What is a 9 digit number using digits 1-9 that is divisible by 9, if you take away the last digit is divisible by 8 etc
+6251 you can build this up from the left
one such number is
123654321
$${\frac{{\mathtt{123\,654\,321}}}{{\mathtt{9}}}} = {\mathtt{13\,739\,369}}$$
$${\frac{{\mathtt{12\,365\,432}}}{{\mathtt{8}}}} = {\mathtt{1\,545\,679}}$$
$${\frac{{\mathtt{1\,236\,543}}}{{\mathtt{7}}}} = {\mathtt{176\,649}}$$
$${\frac{{\mathtt{123\,654}}}{{\mathtt{6}}}} = {\mathtt{20\,609}}$$
$${\frac{{\mathtt{12\,365}}}{{\mathtt{5}}}} = {\mathtt{2\,473}}$$
$${\frac{{\mathtt{1\,236}}}{{\mathtt{4}}}} = {\mathtt{309}}$$
$${\frac{{\mathtt{123}}}{{\mathtt{3}}}} = {\mathtt{41}}$$
$${\frac{{\mathtt{12}}}{{\mathtt{2}}}} = {\mathtt{6}}$$
$${\frac{{\mathtt{1}}}{{\mathtt{1}}}} = {\mathtt{1}}$$
if you just work this backwards you can see how it's constructed. Just make sure your condition is met each time you add a new digit.
+6251 you can build this up from the left
one such number is
123654321
$${\frac{{\mathtt{123\,654\,321}}}{{\mathtt{9}}}} = {\mathtt{13\,739\,369}}$$
$${\frac{{\mathtt{12\,365\,432}}}{{\mathtt{8}}}} = {\mathtt{1\,545\,679}}$$
$${\frac{{\mathtt{1\,236\,543}}}{{\mathtt{7}}}} = {\mathtt{176\,649}}$$
$${\frac{{\mathtt{123\,654}}}{{\mathtt{6}}}} = {\mathtt{20\,609}}$$
$${\frac{{\mathtt{12\,365}}}{{\mathtt{5}}}} = {\mathtt{2\,473}}$$
$${\frac{{\mathtt{1\,236}}}{{\mathtt{4}}}} = {\mathtt{309}}$$
$${\frac{{\mathtt{123}}}{{\mathtt{3}}}} = {\mathtt{41}}$$
$${\frac{{\mathtt{12}}}{{\mathtt{2}}}} = {\mathtt{6}}$$
$${\frac{{\mathtt{1}}}{{\mathtt{1}}}} = {\mathtt{1}}$$
if you just work this backwards you can see how it's constructed. Just make sure your condition is met each time you add a new digit.
