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
Cockroaches have 6 feet, mice have 4, and birds have 2. They each have one head.

Answer
35 birds, 5 mice, and 10 cockroaches.

Reasoning
Cockroaches have 6 feet, mice have 4, and birds have 2. They each have one head.

We can write down expressions for the heads and the feet, calling birds B, mice M, and cockroaches C.

Counting the heads:
(1)    B +  M +  C =  50

Counting the feet:
(2)   2B + 4M + 6C = 150

We are told that for every mouse there are two cockroaches so, C = 2M. Update (1) and (2) to give:
(3)    B +  3M =  50
(4)   2B + 16M = 150

If we double (3) we get:
(5)   2B +  6M = 100

We can now do (4) – (5) to give:
 10M = 50
   M = 5

So, we have 5 mice (and 10 cockroaches).

We can use M = 5 in (3) to give:
 B + 3 x 5 = 50
    B + 15 = 50
         B = 35

So, C = 10, M = 5 and B = 35.

Double-Checking
10 cockroaches have 10 heads and 60 feet.
5 mice have 5 heads and 20 feet.
35 birds have 35 heads and 70 feet.

The total number of heads = 10 + 5 + 35 = 50.

The total number of feet = 60 + 20 + 70 = 150.

Workings

Hint
The words are linked by their letters.

Answer
Approved.

The initial letters spell ORANGE and the last letters spell INDIGO.

Workings

Hint
Where did Reed come in game 1?

Answer
Name     #1  #2
Kelly     1   2
Reed      2   1
Jamie     3   4
Sam       4   3

Reasoning
In Game1, (Clue1) Reed beat Jamie, and (Clue3) Jamie beat Sam.

   Game1: Reed, Jamie, Sam

Since (Clue3) Reed won Game2 , and (Clue4) no player got the same placing twice, Reed can't have won Game1, therefore Kelly did.

   Game1: Kelly, Reed, Jamie, Sam

In Game2:
   Reed won (Clue3).
   Sam can't have come last again (Clue4).
   Since Kelly beat Sam (Clue1), Sam can only have come third.

   Game2: Reed, Kelly, Sam, Jamie