Random Puzzles 

Workings

Hint
Going down and across the floor isn't the only route.

Answer
40 feet.

Explanation Diagram
If you imagine the room to be a cardboard box, you can 'unfold' the room in various ways, and each route gives a different answer.



We can use Pythagoras' theorem (a² + b² = c²) to calculate the distances:
   distance² = horizontal² + vertical²
   distance = √(horizontal² + vertical²)

Route #1
   distance = 1 + 30 + 11 = 42 feet.

Route #2
   horizontal = 6 + 30 + 6 = 42 feet.
   vertical = 10 feet.
   distance = √(42² + 10²) ≈ 43.174 feet.

Route #3
   horizontal = 1 + 30 + 6 = 37 feet.
   vertical = 6 + 11 = 17 feet.
   distance = √(37² + 17²) ≈ 43.178 feet.

Route #4
   horizontal = 1 + 30 + 1 = 32 feet.
   vertical = 6 + 12 + 6 = 24 feet.
   distance = √(32² + 24²) = 40 feet.

Workings

Hint
Try working backwards.

Answer
175 miles.

The total distance was 180 miles, but as I still had 5 miles to go, the required answer is 175 miles.

Reasoning
Let's try working backwards.

Day 4: I travelled ³/₄, which means that the other ¹/₄ was 5 miles, and 20 miles were left at the start of day four.

Day 3: I travelled ²/₃, which means that the other ¹/₃ was 20 mile, and 60 miles were left at the start of day three.

Day 2: I travelled ¹/₂, which means that the other ¹/₂ was 60 miles, and 120 miles were left at the start of day two.

Day 1: I travelled ¹/₃, which means that the other ²/₃ was 120 miles, and 180 miles were ahead at the start of day one.

The full distance was therefore 180 miles, but we were asked how many miles I had travelled so far, and as I still had 5 to go the answer is 175 miles.

Double-Checking
Start distance: 180 miles.

Day 1: I travelled ¹/₃ of the distance (60 miles), leaving 120 miles.

Day 2: I travelled ¹/₂ of the distance (60 miles), leaving 60 miles.

Day 3: I travelled ²/₃ of the distance (40 miles), leaving 20 miles.

Day 4: I travelled ³/₄ of the distance (15 miles), leaving 5 miles.

Workings

Hint
Try rewriting each statement so that they are all 'finished before' statements instead.

Answer
Bailey won …

… then Dale, Alex, Chris, and Emery.

Reasoning
By placing the person who finished higher to the left, we have:

Dale finished before Alex (Dale > Alex) Emery finished after Bailey (Bailey > Emery) Alex finished before Chris (Alex > Chris) Emery finished after Dale (Dale > Emery) Bailey finished before Alex (Bailey > Alex) Dale finished after Bailey (Bailey > Dale) Chris finished before Emery (Chris > Emery)
From (1) and (3):

   Dale > Alex > Chris

Adding (7):

   Dale > Alex > Chris > Emery

Adding (6):

   Bailey > Dale > Alex > Chris > Emery

Which is the final placing for all the players, and can be double-checked with the remaining clues.

Workings

Hint
One of answers involves royalty.

Answer
Prince, princes, princess.

Bra, bras, brass.

A similar change is care, cares, caress, but these are not nouns.