Random Puzzles 

Workings

Hint

Answer
726: (n! + n).

Workings

Hint
Try removing the spaces from the sequence.

Answer
1301311 or 1210121.

Reasoning
Removing spaces from the original sequence gives:

   1 23 124 1251 26127 128129

   123124125126127128129

Now adding spaces back in, in the correct place:

   123 124 125 126 127 128 129

The next few terms could be:

   130 131 132
   or
   1210 1211 1212

Add these to the end:

   123 124 125 126 127 128 129 130 131 132
   or
   123 124 125 126 127 128 129 1210 1211 1212

Remove the spaces again:

   123124125126127128129130131132
   or
   123124125126127128129121012111212

Now break the sequence into chunks of increasing size:

   1 23 124 1251 26127 128129 1301311
   or
   1 23 124 1251 26127 128129 1210121

So the missing term is 1301311 or 1210121.

Workings

Hint
How can we write this time and date?

Answer
The time and day became:

12:34 5/6/78 (in UK format)

In US format, this happened on the 6^th of May.

Workings

Hint
Where can the word EASY can be found in the first set of words?

Answer
Hard.

Using the first letter of the first word, the second letter of the second word, etc.