The Library Book Swap Ticket Count
Read this notice from the Aomori City Library. 'Book Swap: Saturday, March 16, 10:00–12:00, Community Room. Bring up to five books in good condition. We cannot accept magazines, textbooks, or damaged books. You receive one ticket for each accepted book, up to three tickets per person. You may choose books from 11:00. Leftover books will be donated. Students who help set up from 9:00 to 9:45 receive one extra ticket.' Yuki arrives at 10:30 with six books: three novels in good condition, two magazines, and one novel with a torn cover. She wants four books. She did not help with setup. She has 2,000 yen, but the swap is free. She plans to leave at 11:20. She wants to choose all four before she leaves.
1. How many tickets will Yuki receive? Show the counting rule and the arithmetic.
Read the worked answer
Count only accepted books. Three novels are in good condition = 3 accepted. The two magazines are explicitly excluded. The torn-cover novel is damaged = excluded. That gives 3 accepted books. The rule is one ticket per accepted book, up to three tickets per person, so the maximum is 3. Yuki did not help with setup, so she gets no extra ticket. Total: 3 tickets. The arithmetic is not 6 − 0 = 6 and not 6 ÷ 2 = 3 by luck; the rule is accepted books, capped at 3.
2. Yuki says, 'I brought six books, so I should get six tickets, or at least four.' Explain why both claims are wrong using the notice.
Read the worked answer
Both claims confuse books brought with tickets earned. The notice says 'one ticket for each accepted book,' not for each book in the bag. Magazines and damaged books are not accepted, so they earn nothing. The second claim-'at least four'-ignores the cap: 'up to three tickets per person.' Even if Yuki brought ten acceptable novels, she would still receive only three tickets. The only extra ticket in the notice is for helping set up from 9:00 to 9:45, which she did not do. So the correct number remains three, and the reason is two separate rules, not one.
3. Can Yuki choose four books at 11:10? Explain what she can do.
Read the worked answer
No. At 11:10 the choosing period has opened (from 11:00), so time is not the problem. The problem is ticket count: Yuki has 3 tickets, and each chosen book costs one ticket, so she can choose at most 3 books. She wants 4. She cannot buy the fourth book because the notice says the swap is free and says nothing about paying; she also cannot earn a fourth ticket now because the cap is 3 and the setup shift has passed. Her realistic options are to choose 3 books and leave at 11:20, or ask a friend who has a spare ticket-but the notice does not say tickets are transferable, so she should not assume that. The safe exam answer is: she can choose 3, not 4.