BrainBashers - Random Puzzles

Puzzle 1

Below you will find 15 well-known five-letter words, with only their endings remaining.

Can you find the words?
--pay --lad --ior --eue --rva --day --voc --yss --gun --pty --til --cay --uke --uze --noe

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Puzzle 2

Student Accommodation - Logic Puzzles

Alex, Bret, Chris, Derek, Eddie, Fred, Greg, Harold, and John are nine students who live in a three storey building, with three rooms on each floor. A room in the West wing, one in the centre, and one in the East wing. If you look directly at the building, the left side is West and the right side is East. Each student is assigned exactly one room. Can you find where each of their rooms is:

Harold does not live on the bottom floor.
Fred lives directly above John and directly next to Bret (who lives in the West wing).
Eddie lives in the East wing and one floor higher than Fred.
Derek lives directly above Fred.
Greg lives directly above Chris.

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???

Puzzle 3

This equation contains the numbers 1-8.

Can you complete it?
6.
.. x
————
....

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Answer
64 x 58 = 3712.

Reasoning
Since no digit is duplicated, neither number can end in 1, otherwise, the last digit of the answer would already have been used.

Neither number can end in 5 because the answer would then end in 5 or 0.

So the first number can only be 62, 63, 64, 67, or 68.

We can now look at what the second number can end with, and we find that …

   if the first number was 62, the second number can only end in 4 or 7.

Why …
   not 1 as previously explained
   not 2 because we've already used that in the 62
   not 3 because 62 x *3 would end in 6, which is already in the 62
   not 5 as previously explained
   not 6 because we've already used that in the 62
   not 8 because 62 x *8 would end in 6, which is already in the 62

We can repeat this for the other possible first numbers and find that …

   if the first number was 62, the second number can only end in 4 or 7.
   if the first number was 63, the second number can only end in 4, 7, or 8.
   if the first number was 64, the second number can only end in 2, 3, 7, or 8.
   if the first number was 67, the second number can only end in 2, 3, or 4.
   if the first number was 68, the second number can only end in 3 or 4.

Let's check these in turn …

If the first number was 62, the only possible values are:

   62 x 14 = 868
   62 x 34 = 2108
   62 x 54 = 3348
   62 x 74 = 4588

or

   62 x 17 = 1054
   62 x 37 = 2294
   62 x 57 = 3534
   62 x 87 = 5394

Only 4 calculations are required for each option, as we didn't need to check 62 x 84 as we already know that the answer would end in 8, or 62 x 47 as we already know that the answer would end in 4.

All of these answers fail as they don't contain all of the digits.

Similarly, we can look at 63, then 64, etc. For each of the numbers, we have to check the possible endings, but in each case, only 4 calculations are required (as seen in the examples above).

We (quickly?) find 64 x 58 = 3712.

Puzzle 4

My trustworthy (?!) BrainBashers word processor is playing its silly tricks again.

This time, it has replaced all of the consonants with random ones.

I can at least be thankful that it has left the vowels untouched.

Can you find all of the animals?
fahjec qsaxe eep zoth epessawx feyuv zowqud pol

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