BrainBashers - Random Puzzles

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Puzzle 197

The Miller next took the company aside and showed them nine sacks of flour that were standing as depicted in the sketch.

"Now, hearken, all and some," said he, "while that I do set ye the riddle of the nine sacks of flour.

And mark ye, my lords, that there be single sacks on the outside, pairs next unto them, and three together in the middle thereof.

By Saint Benedict, it doth so happen that if we do but multiply the pair, 28, by the single one, 7, the answer is 196, which is of a truth the number shown by the sacks in the middle.

Yet it be not true that the other pair, 34, when so multiplied by its neighbour, 5, will also make 196.

Wherefore I do beg you, gentle sirs, so to place anew the nine sacks with as little trouble as possible that each pair when thus multiplied by its single neighbour shall make the number in the middle."

As the Miller has stipulated in effect that as few bags as possible shall be moved, there is only one answer to this puzzle, which everybody should be able to solve.

Sacks 7 28 196 34 5

The Miller's Puzzle, The Canterbury Puzzles, Henry Ernest Dudeney.

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Puzzle 198

At a recent school fayre, 500 people attended and £500 was raised. The prices were as follows:
Fathers £2.00
Mothers £3.00
Children £0.48

More mothers than fathers turned up. How many children were there?

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Puzzle 199

What always weighs the same …

… no matter how large it is?

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Puzzle 200

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.

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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.