Brain Teasers and Puzzles 

Workings

Hint
What could we do with the digits?

Answer
If the sum of the digits is divisible by nine, so is the number.

Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.

For example, is 486451464 divisible by 9?

Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.

Is 42 divisible by 9? Not sure, you can then do:

4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.

Workings

Hint
Albert is 6 years old.

Answer
10 years old.

The length of their name in years.

Workings

Hint
120 = 24 x 5.

Answer
720.

Each term is a factorial, 6! = 1 x 2 x 3 x 4 x 5 x 6 = 720.

Workings

Hint
A tricky base 8 question.

Answer
61.

Each term is a square expressed in base eight, 7 2=49 = 61 in base 8.