Haskell CW II.B2

Review questions:

1. (b1) Make a list of ordered pairs which contain the square and cube of each counting number 1 through 10.

    b1 == [(1,1),(2^2,2^3),(3^2, 3^3),(4^2,4^3), etc. ]
   

2. (b2) Given a number m, write a function b2 to make a list of all of the ordered pairs in b1 where $m$ is in the closed interval $[x,y]$ . That means $x \le m \le y$ . As an example, think of $m=20$ and the ordered pair $(9,27)$ from b1. Since $m=20$ is between $x=9$ and $y=27$ , we would say yes, $m=20$ is in the closed interval $[x=9,y=27]$ . An example with a list of intervals is:

   b2 20 == [(9,27),(16,64)]
   

3. (b3) Given a list of words, make a list of tuples numbering them in reverse order.

   b3 ["school","home","work","beach"] ==
       [(4,"school"), (3,"home"), (2, "work"), (1,"beach")]
   

4. (b4) Using a trial and error method, find all of the integer solutions $(x,y)$ to the equation

   $$55x+34y=1$$

   that have $-100\le y\le 500$ . The list has 11 points and includes $(-123,199)$ .

5. (b5) Given a list of words, extract the ones with at most 6 letters into a new list.

   b5 ["a","by","cap","deal","egret","furies","gallant","hieroglyphics","x"]
     == ["a","by","cap","deal","egret","furies","x"]
   

6. (b6) Suppose a 10x10 rectangle has two radius 5 circles inside it, one centered at (7,5) and the other centered at (3,5). Estimate the probability that a random point will be inside at least one of the circles by making a grid of squares 0.1x0.1 covering the whole rectangle and counting how many points are inside at least one of the circles.