Brain Teasers and Puzzles 

Workings

Hint
A little bit of algebra might help.

Answer
There are four boys and three girls.

If we call the number of boys B, and girls G.

From the first statement (we take one off as Daniel is a boy):

              B - 1 = G

and similarly:

        2 x (G - 1) = B

Substitute G from the first equation into the second equation to give:

  2 x ((B - 1) - 1) = B

    2 x (B - 1) - 2 = B

      2 x B - 2 - 2 = B

          2 x B - 4 = B

                  B = 4

which means that B = 4 and hence G = 3.

Workings

Hint
These are the first letters of the words: N, C, C, C, E, H, O, C, L, M.

Answer
new + sag + ent = newsagent
cro + cod + ile = crocodile
col + lis + ion = collision
cla + ssr + oom = classroom
enc + our + age = encourage
hai + rbr + ush = hairbrush
oth + erw + ise = otherwise
clo + sen + ess = closeness
lig + htn + ing = lightning
mar + gar + ine = margarine

Workings

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.

Workings

Hint
The first 5 words begin with D, A, E, W, T.

Answer
--lta = delta --yss = abyss --pty = empty --dth = width --day = today --ybe = maybe --dex = index or codex --fth = fifth --nda = panda --aph = graph --alp = scalp --era = opera --njo = banjo --eue = queue --xty = sixty