Puzzle 237
What number comes next in this sequence:
1 4 8 13 21 30 36 {?}
Puzzle Copyright © Kevin Stone
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Hint
Try writing the numbers out as letters.
Answer
45.
Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1 + length("ONE") = 4
4 + length("FOUR") = 8
8 + length("EIGHT") = 13
13 + length("THIRTEEN") = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY") = 36
36 + length("THIRTYSIX") = 45
Puzzle 238
Consider an arrow in flight towards a target.
At any given moment of time, a snapshot could be taken of this arrow. In this snapshot, the arrow would not be moving. Let us now take another snapshot, leaving a very small gap of time between them. Again, the arrow is stationary. We can keep taking snapshots for each moment of time, each of which shows the arrow to be stationary. Therefore the overall effect is that the arrow never moves, however it still hits the target!
Where lies the flaw in the logic?
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This is a puzzle to melt the brain!
Answer
The arrow clearly reaches the target.
This is a classic paradox, attributed to Zeno of Elea, a Greek philosopher from Italy. Great minds over the centuries have pondered this paradox, and the scope of a solution is beyond the space available here. It is not even clear that a solution to the paradox actually exists.
Puzzle 239
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.
Puzzle Copyright © Rodins Ltd
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Hint
Determine who shared which room with whom.
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.
Puzzle 240
What is the minimum number of queens required on a chessboard such that all squares are attacked?
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Try this with a real board.
Answer
5 queens are required.
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