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Reasoning
The easiest way to solve this puzzle is to use Q1 to check the logic.
If Q1's answer was A, this tells us that Q2's answer is B, which tells us Q3's is D, which tells us Q4's answer is B, which tells us Q1's answer is C. A contradiction.
If Q1's answer was B, this tells us that Q2's answer is A, which tells us Q3's is C, which tells us Q4's answer is C, which tells us Q1's answer is A. A contradiction.
If Q1's answer was C, this tells us that Q2's answer is D, which tells us Q3's is A, which tells us Q4's answer is D, which tells us Q1's answer is B. A contradiction.
If Q1's answer was D, this tells us that Q2's answer is C, which tells us Q3's is B, which tells us Q4's answer is A, which tells us Q1's answer is D. Which is correct, and therefore the correct answer.
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Puzzle 190
I started out on the journey from the forest with a full tank of fuel, 12 gallons exactly.
However, the moment I started out, the fuel tank sprung a leak. I travelled at 50 mph until I ran out of fuel exactly 4 hours later.
I know that the car does 25 miles for each gallon.
Reasoning
I travelled at 50mph for 4 hours, which is 200 miles.
I used 25 gallons every 25 miles, so I used 8 gallons travelling those 200 miles.
I started with 12 gallons and used 8 gallons, so I lost the other 4 gallons.
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Puzzle 191
These five business people represented different companies at a recent trade fair. Unfortunately, the hotel they were all due to stay in had accidentally double booked their rooms. They tried other hotels in the area but all were fully booked. Consequently, they all agreed to share the only two rooms available in the hotel, one twin and one triple.
From the clues, can you work out each person's name, company and official title?
When the five realised their dilemma, they drew straws to see who would share with whom. The outcome for four of them was that the CEO shared with the business person from ABM Inc. and Glenn shared with the Developer. Alex does not work for Reed Right and is not the Director. The Director does not work for Lantel or Blue Teeth. Neither Clarkson nor Grimaldi works for Reed Right. Grimaldi is either the IT Analyst or the CEO. The business person from Reed Right did not share a room with Taylor. Clarkson, who does not work for Lantel, shared with either Taylor or Grimaldi but not both. Glenn's surname is either Casson or Graves. Glenn did not share with Charlie. The business person from Chiptech shared with the business person from Lantel. The CEO shared with the IT Analyst. Casson works for either Blue Teeth or Chiptech. Neither Jesse nor Alex works for ABM Inc. Fielder shared with the Director. The business person from Blue Teeth shared with the Developer.
First names : Alex, Charlie, Glenn, Jesse, Taylor.
Last names : Casson, Clarkson, Fielder, Graves, Grimaldi.
Company : ABM Inc., Blue Teeth, Chiptech, Lantel, Reed Right.
Position : Accountant, CEO, Developer, Director, IT Analyst.
Answer First Last Name Company Position Charlie Grimaldi ABM Inc. IT Analyst Glenn Casson Chiptech Director Jesse Graves Reed Right CEO Alex Clarkson Blue Teeth Accountant Taylor Fielder Lantel Developer
To solve this puzzle, you first need to determine who shared which room with whom. Three delegates shared the triple and two shared the twin. The CEO shared with the business person from ABM in one room and Glenn shared with the Developer in the other (1). Since Grimaldi is either the IT Analyst or the CEO (3) and the CEO shared with the IT Analyst, Grimaldi is in the same room as whoever is the CEO, IT Analyst and ABM delegate although Grimaldi could have been one of these people. Glenn did not share with Charlie (6) so Charlie is in the same bedroom as, and possibly is, the CEO, IT Analyst, Grimaldi and/or the ABM delegate. Grimaldi and Taylor were in different rooms so Taylor shared a room with Clarkson (5) and the Reed Right delegate was in a different room to Taylor. At this stage we know:
Room 1
CEO
IT Analyst
ABM delegate
Grimaldi
Charlie
Reed Right delegate
Room 2
Glenn
Developer
Taylor
Clarkson
Since the Chiptech delegate shared with the Lantel delegate (7), both of these must have been in room 2 otherwise there would be four delegates in room 1 which is not possible.
Now this has been ascertained, the puzzle can be solved:
The CEO shared with the IT Analyst so the IT Analyst must work for ABM (Clues 1 and 8) so the CEO must work for Reed Right. Since Grimaldi does not work for Reed Right, they must be the IT Analyst. Clarkson, Fielder and Casson are in room 2 so the CEO must be Graves. Graves is not Glenn (1), Taylor (4), Charlie (IT Analyst) or Alex (2) so must be Jesse. Clarkson is not Taylor (5), Glenn (6), Charlie or Jesse (in room 1) so must be Alex. The Director does not work for Lantel or Blue Teeth (2), Reed Right or ABM (room 1) so must work for Chiptech. This is not Graves or Grimaldi (room 1), Clarkson (2) or Fielder (11) so must be Casson. Since Graves' first name is Jesse, Casson must be Glenn (6). Alex Clarkson does not work for Reed Right or ABM (room 1), Lantel (5) or Chiptech so must work for Blue Teeth. Since they are not the Developer (12) they must be the Accountant. This leaves Taylor Fielder who is the Developer for Lantel.
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Puzzle 192
In the illustration we have a sketch of Sir Edwyn de Tudor going to rescue his love, who was held captive by a neighbouring wicked baron.
Sir Edwyn calculated that if he rode at fifteen miles an hour he would arrive at the castle an hour too soon, while if he rode at ten miles an hour he would get there just an hour too late.
Now, it was of the first importance that he should arrive at the exact time appointed, in order that the rescue that he had planned should be a success, and the time of the tryst was five o'clock, when the captive would be taking afternoon tea.
The puzzle is to discover exactly how far Sir Edwyn de Tudor had to ride.
Sir Edwyn De Tudor – Amusements In Mathematics, Henry Ernest Dudeney.
If Sir Edwyn left at noon and rode 15 miles an hour, he would arrive at four o'clock – an hour too soon. If he rode 10 miles an hour, he would arrive at six o'clock – an hour too late. But if he went at 12 miles an hour, he would reach the castle of the wicked baron exactly at five o'clock – the time appointed.
The text above is the answer given in the book, and below is a method of finding the answer.
If we call the distance to the castle, D and use the fact that Time = Distance ÷ Speed, we have:
Travelling at 15 mph:
Time1 = D ÷ 15 (an hour too soon)
Travelling at 10 mph:
Time2 = D ÷ 10 (an hour too late)
The time gap between these two times is 2 hours, therefore
Time2 – Time1 = 2
D ÷ 10 – D ÷ 15 = 2
Multiply throughout by 30:
3D – 2D = 60
D = 60 miles.
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
