s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Q are in s(99)? Choose the correct answer
A) Q=350  B) Q=353  C) Q=354  D) Q=356  E) 357
Focus on the points where the number of digits Q in squares change:   1, 2, 3 - Single digit squares. First 2 digit number is 10.   4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.   10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.   32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.   So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272= 
<gadget id="calculator">3 + 12 + 66 + 272</gadget>
<output>353</output>
353.Q=353
<result>B</result>
s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Q are in s(99)?