Random Puzzles 

Workings

Hint
Try removing the spaces and punctuation.

Answers
ROME OR OSLO? ANDREW, JULIE, TO VISIT.
ROMEO ROSLO AND REW JULIET OVISIT
   = ROMEO AND JULIET

WARM TOO FEW, THE SUBWORLD SNEEZES
WAR MTO OF EW THE SUB WORLDS NEEZES
   = WAR OF THE WORLDS

AN I MALL? SHOPS, FAR MALLS?
ANIMAL LSHOPS FARM ALLS
   =ANIMAL FARM

GO NEXT, GO! WITHOUT OTHER I DWINDLE. GO!
GONE XTGO WITH OUTO THE RID WIND LEGO
   = GONE WITH THE WIND

WATER. SHIP, BOAT. STORM! DOWN RAIN!
WATERSHIP BOATSTORM DOWN RAIN
   = WATERSHIP DOWN

BRAVERY IN A NEW AGE, WORLD'S HOPE.
BRAVE RYINA NEW AGE WORLD SHOPE
   = BRAVE NEW WORLD

Workings

Hint
How many leaves will I have collected on day 5?

Answer
On the 23^rd.

Reasoning
We could simply keep adding until we get the required number:

   1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23

   = 276 leaves.

But a more mathematical method might help to answer the Bonus Question, as this might take a while if we keep adding!

So, let's create a method by imagining that we are adding the numbers from 1 to 30.

   1 + 2 + 3 + … + 28 + 29 + 30

If we now take the numbers in pairs, taking one from each end, we have:

   (1 + 30) + (2 + 29) + (3 + 28) + … + (15 + 16)

Each pair adds to 31, and we have 15 pairs. So the total sum is 31 x 15 = 465.

The total sum from 1 to any number (N) can be found using this technique, and we will have:

   Each pair adds to (1 + N), and there are N ÷ 2 pairs. So the total is:

   (1 + N) x  N
             ———
              2

In this puzzle, we know that this equals 276.

So:

   (1 + N) x  N = 276
             ———
              2

We can expand the brackets, and multiply both sides by 2, to give:

   N + N² = 552

Rearranging we get:

   N² + N − 552 = 0

And 552 = 2 x 2 x 2 x 3 x 23, so this can be factorised as:

   (N + 24) x (N − 23) = 0

Because we need to find a positive number of days, the only possible answer is:

   (N − 23) = 0

So N = 23 days.
Bonus Question

To answer the bonus question, we have:

   (1 + N) x  N = 56616
             ———
              2

Rearranging we get:

   N² + N − 113232 = 0

And 113232 = 2⁴ x 3 x 7 x 337, so this can be factorised as:

   (N − 336) x (N + 337) = 0

Because we need to find a positive number of days, the only possible answer is:

   (N − 336) = 0

So N = 336 days (I did say that I liked collecting leaves!).

Workings

Hint
Albert is 6 years old.

Answer
10 years old.

The length of their name in years.

Workings

Hint
Start with Betty, Mrs Kipper, and Ada, as these are three different people.

Answer
             Now     Last
Annie Ford   Red     Green
Betty Jester Blue    Red
Cybil Long   Green   Yellow
Diane Kipper Yellow  Blue

Reasoning
By (3), Betty currently has Blue flowers.
             Now     Last
Betty        Blue

By (4), Mrs Kipper currently has Yellow flowers, and used to have Blue.
             Now     Last
Betty        Blue
      Kipper Yellow  Blue

By (5), we know Annie Ford's name.
             Now     Last
Betty        Blue
      Kipper Yellow  Blue
Annie Ford

By (6), Mrs Kipper must be Diane, and the remaining person's name is Cybil.
             Now     Last
Betty        Blue
Diane Kipper Yellow  Blue
Annie Ford
Cybil

By (2), whoever currently has the Green flowers used to have Yellow, but by (5) this can't be Annie Ford, so this must be Cybil. Which means that Annie must currently have the Red flowers.
             Now     Last
Betty        Blue
Diane Kipper Yellow  Blue
Annie Ford   Red
Cybil        Green   Yellow

By (3), Betty isn't Mrs Long, so must be Mrs Jester. Therefore Cybil must be Mrs Long.
             Now     Last
Betty Jester Blue
Diane Kipper Yellow  Blue
Annie Ford   Red
Cybil Long   Green   Yellow

By (1), Annie Ford must have previously had Green, and Betty Jester had Red.
             Now     Last
Betty Jester Blue    Red
Diane Kipper Yellow  Blue
Annie Ford   Red     Green
Cybil Long   Green   Yellow