Random Puzzles 

Workings

Hint
A very tricky puzzle involving prime numbers.

Answer
101.

These are prime numbers, which, when reversed, are also prime.

Workings

Hint
You would probably never try this.

Answer
An umbrella.

Workings

Hint
The answer isn't very large at all.

Answer
There are four boys and six girls in the family.

If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b − 1) = g.

And his sister, Frankie, has one more sister than she has brothers, so g − 1 = b + 1.
    2(b − 1) = g       [1]
       g − 1 = b + 1   [2]

Using [1] in [2] gives:

2(b − 1) − 1 = b + 1

Expanding the bracket gives:

  2b − 2 − 1 = b + 1

Simplifying the left hand side gives:

     2b − 3  = b + 1

Add 3 to each side gives:

          2b = b + 4

Subtract b from both sides gives:

           b = 4

Using b = 4 in [1] gives:

    2(4 − 1) = g

           6 = g

Workings

Hint
How many sweets in total are there?

Answer
1 in 15.

Reasoning
In total, there are 390 sweets in the jar, and 26 of them are blue.

So the chance of picking blue is 26 in 390 = 1 in 15 = 6.66%.