Chapter 5, Problem 33PE

You and your friends decided to hold a “Secret Santa” gift exchange, where each person buys a gift for someone else. To see how this whole thing works, let’s consider the following example. Suppose there are 7 people A, B, C, D, E, F, and G. We denote x → y to mean “x gives a gift to y.” If the gift exchange starts with person A, then they give a gift to E. Then E gives a gift to B. And it is entirely possible that B gives a gift to A; in such a case we have completed a “cycle.” In case a cycle occurs, the gift exchange resumes with another person that hasn’t given their gift yet. If the gift exchange resumes with person D, then they give a gift to G. Then G gives a gift to F. Then F gives a gift to C. Then finally C gives a gift to D, which completes another cycle. Since all of the people have given their gifts, the giftexchange is done, otherwise the gift exchange resumes again with another person. All in all, there are two cycles that occurred during the gift exchange: A → E → B → A…

Suppose a person can buy a chocolate bar from the vending machine for $1 each.  Inside every chocolate bar is a coupon.  A person can redeem 3 coupons for one chocolate bar from the machine.  This means that once a person has started buying chocolate bars from the machine, he/she always has some coupons. A person would like to know how many chocolate bars can be bought, if a person starts with N dollars and always redeem coupons, if he/she has enough for an additional chocolate bar. For example: With 3 dollars a person could buy 4 chocolate bars after purchasing 3 bars giving him/her 3 coupons and then redeeming the 3 coupons for one bar.  This would leave him/her with one extra coupon. Thus, will have 4 chocolate bars and still have one coupon leftover. For 11 dollars, a person can have 16 chocolate bars and still have one coupon leftover.  For 12 dollars, a person can have 17 chocolate bars and have two coupons leftover. Write a complete Python program that prompts a buyer to input…

In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case contains…