Solution to Problem 6, Test 2 Suppose that two numbers n and n' has the same remainders when divided by 10 and when divided by 16. This means that their difference n-n' is divisible by 10 and 16, and thus, divisible by their least common multiplier lcm(10,16) = 80. As we discussed in class, you can find lcm(a,b) as the ratio (a*b)/gcd(a,b), in this case (10*16)/2 = 80. So, if you have two different numbers with the same remainders mod 10 and mod 16, the difference is divisible by 80. The length of the whole interval [20,90] is 70, so on this interval, we cannot have two numbers whose different is 80 or more - and therefore, the reconstruction is unique. The answer to this question would be different if we had a different age interval, e.g, [0,90]. In this case, for numbers 10 and 90 on this interval, the difference is divisible by 80 and hence, both numbers have the same remainders when divided by 10 and by 16.