The Dice Date Indicator!

How can you represent days of month using two 6 sided dice? You can write one number on each face of the dice from 0 to 9 and you have to represent days from 1 to 31, for example for 1, one dice should show 0 and another should show 1, similarly for 29 one dice should show 2 and another should show 9.

This is how it can be indicated!

Making of The Dice Date Indicator

What was the challenge?

Dice 1: 0 1 2 3 5 7

Dice 2: 0 1 2 4 6 8

The number 0 has to be present on both the dice. The '0' on first die needed for dates from 1 to 9 to show them as 01,02,03......and the '0' on second die will be used for the dates 10,20,30.

The number 1 and 2 are repeated on the dates 11 and 22 so those 2 numbers has to be there on both dice.

Now, we are left with total 6 positions but 7 numbers - 3 to 9.

However, 6 and 9 can be represented by single die if it is written on one of the side of the die. In normal position it will represent 6 & in inverted position it will show 9 or say vice versa.

For example, the dates 6 and 9 can be indicated as - 

A Verbal Arithmetic Puzzle

In this equation, each of the letters represents uniquely a different digit in base 10:

YE × ME = TTT.

What is E + M + T + Y?

Here is solution!

A Verbal Arithmetic Puzzle - Solution

What was the puzzle?

Let's recall the original equation.

YE × ME = TTT.

Obviously, answer TTT is product of T x 111 = T x 3 x 37. 

So YE/ME = 37 and T x 3. Either way, E = 7.

And other number T x 3 is a 2-digit number with 7 at it's unit's place.

So that has to be 9 x 3 = 27.

Therefore,

YE (or ME ) = 37 and ME (or YE) = 27

Hence,
 
E + M + T + Y = 7 + 3 + 9 + 2 = 27.

The Number Game!

Let’s play a game. You name an integer from 1 to 10. Then we’ll take turns adding an integer from 1 to 10 to the number our opponent has just named, giving the resulting sum as our answer. Whoever reaches 100 first is the winner.

You go first. What number should you choose?

This is how you can be winner!

Winning The Number Game!

What was the game?

Here the player whose number 'forces' sum to fall in range of 90-99 will be ending on losing side. 

That means, somehow if you 'force' the total at some point to 89 then opponent has to fall in the range of 90-99 with his number. 

To get 'door' to total 89 you have to force the previous sum to 78 so that opponent is forced to open a 'door' for total 89 for you.

And so on backward you have to make stops at 67, 56, 45, 34, 23, 12, 1.

So you have to start with 1 & achieve all above milestones.

Let's verify our conclusion. Suppose you started with 1.

You       Sum      Opponent    Sum

1            -             8              9
3           12            5              17
6           23            7              30
4           34            9              43
2           45            4              49
7           56            10            66
1           67            3              70
8           78            2              80
9           89            4              93
7           100           

YOU WIN!