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!

Search Number for '?'

Can you find the number for the '?' ?

Skip to the answer! 

In The Search of Number for '?'

Here is the question! 

First two equations clearly indicates it must be straightforward a + b equation.

Now if you observe closely all the equations, then you can find that the number never exceeds 8. So there are chances that all these number are in octal number system i.e. base 8 numbers.

Hence 11 in third equation is actually 8 in decimal. That's why 7 + 8 = 15 where decimal 15 is converted to octal 17. 

Verifying third equation as 15 + 16 = 31 in decimal is actually 17 + 20 = 37.

On the similar note, we have fourth equation in decimal as 31 + 32 = 63 which can be converted to octal as 37 + 40 = 77.

Hence the search for number in place of '?' ends with the number 77.

Even/Even x Even - Odd ?

Can an even number, divided by another even number, times another even number ever equal an odd number?

The three even numbers can be different numbers.



Did you too think same? 

Even/Even X Even = Odd!

What was the question?

Absolutely, it's possible! Take a look at the examples below.

Totally depends on the what result of Even/Even comes out & what is the Even number that is being multiplied with the result.

Forgotten Bank Account Number

Today, John has to transfer 50 euro to the bank account of a Dutch friend. He has written down the account number on a piece paper. But since he had forgotten to take out the paper from his trousers when he put them in the washing machine, one digit of the bank account number became unreadable. The note says: 3170?4847. 

The friend of John is climbing the Mount Everest at the moment, so it is impossible for John to call his friend. Suddenly he remembers that a for a valid Dutch bank account number it holds that the first digit times 9 + the second digit times 8 + the third digit times 7 + ...... + the ninth digit times 1 should be divisible by 11. John thinks for a moment and finds the correct number. 

What is it? 

That it is !

Recalling Forgotten Bank Account Number

What were the clues? 

Let x be that missing digit. Then the bank account number looks like, 3170x4847.

Now 9 x First Digit + 8 x Second Digit + 7 x Third Digit.......must be divisible by 11.

That is 27 + 8 + 49 + 0 + 5x + 16 + 24 + 8 + 7 = 139 + 5x must be divisible by 11. 

The only value of x as a digit the satisfies above is 3. With that, total sum 154 is divisible by 11.

Hence, the account number must be, 317034847. 

 

What's Next in the Series?

Can you find the next number in series?
5, 8, 17, 47, 242, ? 

And this should be the next number!

Source 

The Next Number In The Series

What was the series?

Let's take a look at the series once again.

5, 8, 17, 47, 242, ? 

Here if we observe carefully, we can notice that,

5^2 - 8 = 17
8^2 - 17 = 47
17^2 - 47 = 242


In short, (n the number) = [Square of (n-2) th number] - [(n-1) th number].

Hence,

47^2 - 242 = 1967.  

I Found! Did you?

Just Try To Crack It!

Can you tell the correct key?

Here is the step-by-step process!

Source 

Cracking of The Code in Steps...

What was the challenge?

Let's number the clues as 1, 2, 3.

Now following step by step process here onward. 

1. The numbers 3 & 1 are common in first & third combinations. Now both must not be the part of original number as in that case Clue 1 will be invalid. 

2. If numbers 3 & 1 are not correct in third combination then the correct 2 numbers must be among 5,7,9.

3. But it can't be both 7 and 9 as again that would make clue 1 invalid! Hence, the 5 is part of the original key & in correct position as in third combination. So we have got first digit of key as a 5.

4. The 1 correct number in clue 2 is 5 & that's in wrong position. If other is assumed to be 9 & to be in right position then it contradict the clue 3. So the second digit must be 7.

5.The only correct number in clue 1 is 7 & that's in wrong position. That means numbers 1,3,4,9 must not be the part of the code.

6. Since 3,4,9 eliminated in previous steps, the only number that is correct and in right position must be 6 in suggestion made by clue 2. So far we have got 3 digits of the code as 576XX.

7. Last 2 digits can be any combination from 0,2,5,7,6,8. Now addition of all digits is equal to the number formed by last 2 digits. It's impossible that the addition of all digits exceeds 50. Hence, the second last digit must be 2.

8. Now both 57620 or 57628 are perfectly valid where sum of all digits equals to number formed by last 2 digits. 

  

Remove Matches To Match Number

Remove six matches to make 10.

Shown here how it can be done!

  

Matches To Match Number

What was the challenge? 

It's pretty simple one. Nowhere it is mentioned that you have to make it as 

10 & not allowed to make TEN. So three sticks from first, one from second & 

2 from third gives us TEN.

However, we can make it as 10 as well. Removing 1 stick from first, 4 from 

second & 1 from third produces 10.