Different Kind of Dice Game!

Timothy and Urban are playing a game with two six-sided dices. The dice are unusual: Rather than bearing a number, each face is painted either red  or blue.

The two take turns throwing the dice. Timothy wins if the two top faces are the same color, and Urban wins if they’re different. Their chances of winning are equal.

The first die has 5 red faces and 1 blue face. What are the colors on the second die?

The second die must have 'these' colors!

Die Needed For Different Kind of Dice Game!

What was the different in dice game?

Throwing two six-sided dice produces 36 possible outcomes. Since both Timothy and Urban have equal chances of winning, there are 18 outcomes where top faces are of same color.

Let's assume there are 'x' red faces and (6-x) blue faces on the other dice.

Remember, the first die has 5 red faces and 1 blue face. Then there are 5x ways by which top faces are red & 1(6-x) ways by which they both are blue. But as deduced above, there are 18 such outcomes in total where faces of dice matches color.

Therefore,

5x + 1(6-x) = 18

4x = 12

x = 3

Hence, other die have 3 red colored & 3 blue colored faces.

Identify The Cards

From a pack of 52 cards ,I placed 4 cards on the table.

I will give you 4 clues about the cards:

Clue 1: Card on left cannot be greater than card on the right.
Clue 2: Difference between 1st card and 3rd card is 8.
Clue 3: There is no card of ace.
Clue 4: There is no face cards (queen,king,jacks).
Clue 5: Difference between 2nd card and 4th card is 7.

Identify four cards ?

Cards identified here!

Source 

Identified Cards From Clues

What was the task given? 

Let's list the clues once again here for our convenience.

Clue 1: Card on left cannot be greater than card on the right.
Clue 2: Difference between 1st card and 3rd card is 8.
Clue 3: There is no card of ace.
Clue 4: There is no face cards (queen,king,jacks).
Clue 5: Difference between 2nd card and 4th card is 7.

From Clue 4, it's very clear that there is no King, Queen or Jack card.

From Clue 2 & Clue 3, we have combinations of either 1,9 or 2,10 at first & third place. But Clue 3 eliminates the combination of 1,9.So at first place we have 2 & at third we have 10.

Again from Clue 5 & Clue 3, possible combinations at second & fourth place are 2,9 & 3,10. If it was 2,9 then 4 cards would have been like 2,2,10,9. But according to Clue 1 the card on left can't be greater than that at right. Here, the card at third place (10) is greater than that at fourth place (9) placed at right. Hence, this would be invalid combination.

Hence the correct combination for the second & fourth place is 3,10.

So we have 4 cards as 2,3,10,10.