Random Puzzles 

Workings

Hint
It will take a while to check 1 x 7, 2 x 7, 3 x 7. What do we know about the answer?

Answer
63,492 x 7 = 444,444

Reasoning
We can work backwards, as we know that the number multiplied by 7 has only 4's. We can try the following:
      4 ÷ 7 ≈ 0.57     x
     44 ÷ 7 ≈ 6.29     x
    444 ÷ 7 ≈ 63.43    x
  4,444 ÷ 7 ≈ 634.86   x
 44,444 ÷ 7 ≈ 6,349.14 x
444,444 ÷ 7 = 63,492

Workings

Hint
The missing word is two letters long.

Answer
He.

To give:
..ir = heir
..ad = head
..lm = helm
..ed = heed
..lp = help

Workings

Hint
Don't forget the extra 9's in 90, 91, etc.

Answer
300.

Reasoning
Start with: 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 – which is 20 9's.

We then repeat this for 100, 200, 300, up to 900 – which is 200 9's.

But from 900 to 999 we have an extra 100 9's as each starts with a 9.

So the total is 300.

Workings

Hint
One possible answer begins with the letter A.

Answer
ark: bark, dark, market, parking, shark.

or:

ill: bill, dill, millet, pilling, shill.