Random Puzzles 

Workings

Hint
What do the 3 numbers add to, and multiply to, so far?

Answer
$0.50.

Reasoning
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.

The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.

You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.

The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P

    8.50 + P = 18.00 x P

        8.50 = 18.00 x P – P

        8.50 = 17.00 x P

8.50 ÷ 17.00 = P

           P = 0.50.

Workings

Hint
There are fewer than 1,000 apples.

Answer
946 apples.

Reasoning
We know that (answer – 1) is divisible by 3, 5, 7, and 9.

If it's divisible by 9 then it's automatically divisible by 3.

So the number must be a multiple of 5, 7, and 9.

   [5 x 7 x 9 = 315]

Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+1).

Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73 – this doesn't work.

Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36 – this doesn't work.

Let's try 3 x 315 + 1: 946 ÷ 11 = 86 – this works and is the answer.

Workings

Hint
There are no missing letters.

Answer
All good things come to those who wait.

The first and last letters of each word have been exchanged.

Workings

Hint
The 9^th word begins with the letter Q.

Answers
-e-el  = jewel  (JW) b-d    = bad    (A) s-i-l  = skill  (KL) swa--  = swaps  (PS) fo-    = fox    (X) -er-y  = ferry  (FR) a-ur-  = azure  (ZE) -u-dy  = buddy  (BD) -uo-e  = quote  (QT) -e-a-e = menace (MNC) ed--   = edgy   (GY) sc-r-y = scurvy (UV) l-p    = lop    (O) --lls  = hills  (HI)
Alternative Answers
Newel, bad, shill, swaps, fox, jerky, azure, ruddy, quote, became, edgy, scurvy, lop, fills.

Can you find another?