practice problems pending
Q1. All of David's telephone numbers have the form 555−abc−defg, where a,b,c,d,e,f,g are distinct digits and in increasing order, and none is either 0 or 1. How many such numbers are possible? S1. So we have to choose and arrange 7 digits from 8 digits(2 to 9) in increasing order. Or we lay them out in a line first and then remove 1 of them at a time. 8 ways to do that. Answer = 8 Q2. From the set of integers {1,2,3....2009}, choose k pairs {ai, bi} with ai < bi such that so that no two pairs have a common element. Suppose that all the sums ai + bi are distinct and <= 2009. Find the max possible value of 'k'. S2. Let's understand it with a smaller example. Rather than 2009, let's use 9. Each pair's sum <= 9 and each sum is distinct. First instinct: 1+8 2+7 3+6 4+5 The problem is that their sums are not distinct. They are all 9. So let's try something else. If we have to choose 'k' distinct sums each <= 9, what is their max possible sum? 9...
