Random Puzzles 

Workings

Hint
One of the states has 4 letters.

Answer
California, Ohio, and New Jersey.

Workings

Hint
Try working backwards.

Answer
335 strawberries.

Reasoning
Working backwards …

I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.

I ate 6 myself, so I had 108 before I ate those.

I had 108 strawberries, so I had 162 before giving Billie one third.

I ate 3 myself, so I had 165 before I ate those.

I had 165 strawberries, so I had 330 before giving Alex one half.

Ate 5 myself, so I had 335 before I ate those.

Therefore, I started with 335 strawberries.

Double-Checking
I started with 335.

I ate 5, leaving 330.

I gave Alex half (165), leaving 165.

I ate 3, leaving 162.

I gave Billie one third (54), leaving 108.

I ate 6, leaving 102.

I gave Charlie two thirds (68), leaving 34.

Workings

Hint
Remember that there are 12 inches in a foot.

Answer
I asked for 9 foot 2 inches (110 inches) and my friend brought me 2 foot 9 inches (33 inches).

Reasoning
I asked my friend to buy me A feet and B inches, which is a total of 12A + B inches.

He accidentally bought me B feet and A inches, which is 12B + A inches.

We know that 12B + A is actually only 30% of what I wanted, so:

     12B + A = 0.3 x (12A + B)

Multiply throughout by 10:

  120B + 10A = 3 x (12A + B)

  120B + 10A = 36A + 3B

        117B = 26A

           B = 26A ÷ 117

Don't forget that A and B can only be integers, and between 0 and 11.

Since 26 x A has to be at least 117, the lowest possible value for A is 5. We can check the remaining possibilities.
 5 x 26 = 130
 6 x 26 = 156
 7 x 26 = 182
 8 x 26 = 208
 9 x 26 = 234 (*)
10 x 26 = 260
11 x 26 = 286

The only number wholly divisible by 117 is 234, which means that A = 9, and B = 2.

So, I originally asked for 9 feet 2 inches.

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