1.One digit of 970,405 can be changed to make the result divisible by 225. What is the six-digit number after the modification?

2. For each positive integer n, let S(n) denote the sum of the digits of n. How many three-digit n's are there such that n+S(n)+S(S(n)) 0 ≡ mod{9}?

3. A school bought many boxes of $100$ candies each. The teachers opened all the boxes and gave 14 candies to each student, with 2 candies leftover at the end. The receipt shows the school bought 10* boxed boxes of candies where the units digit, represented by *, was covered by a chocolate smudge. How many boxes of candies did the school buy?

Guest Oct 3, 2020