Brain Teasers and Puzzles 

Workings

Hint
The first word begins with the letter J.

Answers
--ust = joust (JO) -ue-n = queen (QE) o-o-e = ozone (ZN) --and = brand (BR) -a-er = water (WT) id-o- = idiom (IM) -uc-y = lucky (LK) e-i-t = exist (XS) hea-- = heavy (VY) tou-- = tough (GH) -rie- = fried (FD) -ry-t = crypt (CP) h-m-n = human (UA)
Alternative Answers
Joust, queen, ozone, brand, wafer, idiom, lucky, exist, heavy, tough, tried, crypt, human.

Can you find another?

Workings

Hint
Could Alex have come first or second in any event?

Answer
   Vault  Beam   Floor
#1 Emery  Chris  Billie
#2 Chris  Billie Emery
#3 Alex   Emery  Chris
#4 Billie Alex   Alex

Reasoning
By (1), Chris came third on the floor. By (6), Billie came last in the vault.
   Vault  Beam   Floor
#1
#2
#3               Chris
#4 Billie

By (2), the athlete who came second in the vault won the beam event, let's mark these as X.
By (3), the athlete who came second on the beam won the floor, let's mark these as Y.
By (5), the athlete who won the vault came second on the floor, let's mark these as Z.
   Vault  Beam   Floor
#1  Z      X      Y
#2  X      Y      Z
#3               Chris
#4 Billie

By (4), Emery beat Alex in every event, therefore Alex can't have won any event, nor come second (because of X, Y, and Z). So, Alex came third on the vault, and last on the floor.
   Vault  Beam   Floor
#1  Z      X      Y
#2  X      Y      Z
#3 Alex          Chris
#4 Billie        Alex

Looking at the vault, Z can't be Chris because Z came second on the floor (but we know Chris came last). So, Z must be Emery, and X is Chris.
   Vault  Beam   Floor
#1 Emery  Chris   Y
#2 Chris   Y     Emery
#3 Alex          Chris
#4 Billie        Alex

Looking at the floor, Y is Billie.
   Vault  Beam   Floor
#1 Emery  Chris  Billie
#2 Chris  Billie Emery
#3 Alex          Chris
#4 Billie        Alex

By (4), Emery beat Alex on the beam.
   Vault  Beam   Floor
#1 Emery  Chris  Billie
#2 Chris  Billie Emery
#3 Alex   Emery  Chris
#4 Billie Alex   Alex

Workings

Hint
How many students study chemistry and physics, but not biology?

Answer
500 students.

Reasoning
The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.

We know that 73 students study all three disciplines, which allows us to work out the numbers.

97 students study chemistry and physics, so 97 – 73 = 24 study just chemistry and physics.
138 students study physics and biology, so 138 – 73 = 65 study just physics and biology.
152 students study chemistry and biology, so 152 – 73 = 79 study just chemistry and biology.

280 students study chemistry, so 280 – 73 – 24 – 79 = 104 study just chemistry.
254 students study physics, so 254 – 73 – 24 – 65 = 92 study just physics.
280 students study biology, 280 – 73 – 65 – 79 = 63 study just biology.

For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.

Workings

Hint
How many 1x1 squares are there?

Answer
91 squares.

Reasoning
Squares of size:
   1 x 1 = 36
   2 x 2 = 25
   3 x 3 = 16
   4 x 4 = 9
   5 x 5 = 4
   6 x 6 = 1

Total = 36 + 25 + 16 + 9 + 4 + 1 = 91.