# Chile to Singapore

Hey guys, I've been into brainteasers since I was little and recently decided to make a puzzle-related website. I figured that this will be the best place to share some of my problems and see if they are any fun. I guess they are too easy, but hope that will entertain you for a bit.

Chile to Singapore

You want to travel from Chile to Singapore. You find two sea captains - Jack and Will, which are willing to board you on their ships. Both of them depart from the same harbor early on the next morning, so you have to decide fast which one to hire. Jack promises that he will arrive in Singapore on the 50th day of the cruise, at midnight. He will charge you $1 per hour for the trip. Will promises that he will also arrive on the 50th day of the cruise, at noon. Will will charge you 1 cent per hour more than Jack. Which captain would you choose? Remark: The first day of the cruise starts when the ship departs the harbor and ends 24 hours later. After that the second day of the cruise begins and so on. P.S. Please, let me know if you have seen identical puzzle elsewhere, don't want to take someone's credit, even accidentally. • Thanks for the feedback qwertylpc. Actually I've made the question ambiguous on purpose, but it is not like "early morning is before midnigh/past noon" or "I want to spend more time on a cruise, so choose the longer one". I hope my answer will make sense eventually. – Puzzle Prime Jul 16 '15 at 19:28 • I would choose the 1.1 dollar cruise, i don't feel like arriving at midnight. And honestly 1.1 dollar is really cheap, I don't mind paying more :) - Welcome to puzzling SE! – Spacemonkey Jul 16 '15 at 19:45 • Haha, thanks Spacemonkey. I guess midnight in Singapore is very pretty though. – Puzzle Prime Jul 16 '15 at 19:51 • Are we really assuming that you want to get there as fast as possible? It is, after all, a cruise. I don't think you'll be suffering the whole way there. – Kingrames Jul 17 '15 at 17:21 • Haha, yeah - the ships are stinky and the food is very bad there. Also, you get sea sickness and the toilets are dirty. – Puzzle Prime Jul 17 '15 at 17:23 ## 5 Answers The journey begins early in the morning. The 50th day starts early morning in Chile, and therefore afternoon/evening in Singapore. This means midnight on the 50th day occurs before noon on the 50th day, so Jack's trip is both faster and cheaper per hour. Choose captain Jack. • Yes! I chose the numbers so that will create some confusion, but was expecting a correct answer sooner. Maybe the formulation was too ambiguous/inaccurate... – Puzzle Prime Jul 16 '15 at 19:50 • Unless early morning means "really really early" morning. Singapore's 11 hours ahead of Chile, so if we're talking before 01:00 early, noon comes first. – Set Big O Jul 16 '15 at 19:51 • @Geobits I thought that Singapore was 11 hours behind Chile. I'll have to double check. – Julian Rosen Jul 16 '15 at 19:52 • AHA! OK, nice puzzle @ArturKirkoryan :-) – Rand al'Thor Jul 16 '15 at 19:54 • @Geobits You are correct. When you Google "time zone chile", it pops up the Easter Island Time Zone. Singapore is 13 hours ahead of that, but only 11 hours ahead of the Chile Time Zone. So hopefully the captains weren't planning the leave before 1:00. – Julian Rosen Jul 16 '15 at 19:55 My assumption is that: Midnight here refers to 00:00, which is the beginning of the day. That would make Jack's trip get in 12 hours earlier than Will's, as well as costing$0.01 less per hour, so it's pretty much a no-brainer that we should take Captain Jack's trip.

• Nope: see the "remark" near the bottom of the OP. Midnight of the 50th day is unambiguously after noon of the 50th day, – Rand al'Thor Jul 16 '15 at 19:19
• I disagree with unambiguously. At least in regards to midnight. – Going hamateur Jul 16 '15 at 19:20
• Oh, hmm. Yeah, you're right. I glossed over that. – Bailey M Jul 16 '15 at 19:20

Fairly straight forward mathing out of this one.

$50\space\text{days} \times 24 \space\text{hours} \times\$1\text{/hour} = \$1200$
$50\space\text{days} \times 24 \space\text{hours} \times\$1.01\text{/hour} = \$1212 - 12\space\text{hours} \times\space\$1.01\text{/hour} = \$1199.88$

Well I don't know about you, but I don't care much for carrying around 88 cents, so probably Captain Will and leave him a 12 cent tip

• Thank you for your response. Unfortunately, the answer is Jack though. – Puzzle Prime Jul 16 '15 at 19:15
• So we are comparing a 1200 hour cruise to a 1188 hour cruise? – Going hamateur Jul 16 '15 at 19:16
• The problem is not very involved and pretty much whatever I say will reveal the correct answer. Not sure if I should say it here... – Puzzle Prime Jul 16 '15 at 19:19
• Okay no need to. – Going hamateur Jul 16 '15 at 19:22

"early on the next morning" isn't very precise; let's say this is $n$ hours before noon. Then Jack will take $n+12+(49\times24)=1188+n$ hours, so he'll charge you $1188+n$ dollars; while Will will take $n+(49\times24)=1176+n$ hours and charge you $(1176+n)\times1.01=1187.76+n+0.01n$ dollars. The difference is $0.01n-0.24$ dollars, which is negative since $n\leq12$. So you should go with Will since he's cheaper.

• Thank you for your response. Unfortunately, the answer is Jack though. – Puzzle Prime Jul 16 '15 at 19:14
• You're assuming that midnight on a given day is at the end of the day, when in fact it is at the beginning. (00:00 is midnight in 24-hour time.) – GentlePurpleRain Jul 16 '15 at 19:29
• @GentlePurpleRain Check the "remark" near the end of the OP. Midnight of the 50th day is after noon of the 50th day, because the 50th day starts some time in the morning. – Rand al'Thor Jul 16 '15 at 19:31
• @randal'thor You're right, I missed that. So a day is defined as the 24-hour period between, say, 6:00 a.m. and 6:00 a.m the next day, which does put midnight after noon on any given day. – GentlePurpleRain Jul 16 '15 at 19:33

The cruise is from Chile to Singapore, so if we didn't change timezones during our travel, Jack would have arrived afternoon and Will REALLY early in the morning, making the latter also slower. Jack is cheaper.