## How many 0’s are present in numbers from 1 to 200 ?

(including both)

Check your answer:-

Click here to See SolutionThus total number of zeros between 1 to 200 are 31.

(including both)

Check your answer:-

Click here to See SolutionHide
One zero after every 10 numbers, thus 20 + 10 extra (for 100’s series, 100, 101 to 109) + 1 extra for 200

Thus total number of zeros between 1 to 200 are 31.

Thus total number of zeros between 1 to 200 are 31.

If we try to make equations

x1 + x2 + x3 = 9

x4 + x5 + 5 = 12

x7 + x8 + x9 = 7

x1 + x4 + x7 = 6

x2 + x5 + x8 = 9

x3 + 5 + x9 = 13

x1 + x5 + x9 = 5

x7 + x5 + x3 = 11

7 variables and 7 equations, its little tough and cumbersome to solve these equations so lets try some hit and trial.

you can see that x1 + x5 + x9 is only 5, thus it has less number of possibilities for x1, x5 and x9 as these cant be -ve.

lets assume x1 and x9 both are 0, in that case x5 will be 5.

17

0 1 8 9

2 5 5 12

4 3 0 7

——

6 9 13 5

diagonal equation does not satisfy, we can see x7 + x5 + x3 exceeds by 6.

so lets try to reduce it by 6,

lets try by x1 = 1, x9 = 1

11

1 1 7 9

4 3 5 12

1 5 1 7

6 9 13 5

it satisfies all the conditions

so, x1 = 1 , x2 = 1, x3 = 7, x4 = 4, x5 = 3, x7 = 1, x8 =5 and x9 = 1

During the African-US summit last year, 10 presidents left the conference room and greeted one another. Assuming no 2 presidents repeatedly greeted themselves, **how many total handshakes were effected?**

Check your answer:-

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Answer is 45 handshakes. The first president greeted 9 presidents, the second 8 and so on, so 9+8+7+6+5+4+3+2+1. This gives 45 handshakes.

in permutations and combinations way

A handshake is possible with two people, so it is similar to How many ways you can select two people out of 10.

i.e. 10C2 = 10!/(8!*2!) = 9*10/2 = 45

A farmer’s wife made some chapatis…the farmer had 3 sons…. The fist son came, gave one chapati to the dog,and made three equal parts of remaining chapatis, ate one part of it and left the other two parts for his brothers….other two sons came one after the other and did the same thinking that they came first…then at night all three came to the house, one of them gave one chapati to dog and made three equal parts and the three brothers ate one-one part of it… If no chapati was broken in pieces then how many minimum number chapatis did the mom made?

Check your answer:-

Lets say their mom made x chapatis

number of chapatis left after first son: 2(x-1)/3

number of chapatis left after second son: 2(2(x-1)/3 – 1)/3 = (4(x-1) – 6)/9 = (4x -10)/9

number of chapatis left after third son: 2((4x -10)/9 -1)/3 = (8x – 20 – 18)/27 = (8x – 38)/27

they ate ((8x-38)/27 -1)/3 chapatis each in the night

number of chapatis left after first son: 2(x-1)/3

number of chapatis left after second son: 2(2(x-1)/3 – 1)/3 = (4(x-1) – 6)/9 = (4x -10)/9

number of chapatis left after third son: 2((4x -10)/9 -1)/3 = (8x – 20 – 18)/27 = (8x – 38)/27

they ate ((8x-38)/27 -1)/3 chapatis each in the night

So it should be an integer value, lets say it is y, where y is an integer.

(8x-38 – 27)/81 = (8x – 65)/81 = y

x = (81*y+ 65)/8 = 10y + (65+y)/8 = 10y + 8 + (y+1)/8

as x should also be an integer

y can be => 7, 15, 23, ….

x can be = 79, 160, 241

minimum value of x is 79.

A*(4+(B/100))=108.81

find the value of (A+B) by solving the above equation

Check your answer:-

Click here to See SolutionHide

A*(4+(B/100)) = 108.81

4A + AB / 100 = 10881/100

4A + (AB/100) = 108 + (81/100)

So,

4A = 108 and AB/100 = 81/100 => AB = 81

Hence

A=108/4=27 and by solving AB 81, B = 3

Thus A+B = 30

**This solution is courtesy Shashikant Soni**

There is four digit number in aabb form and it is a perfect square. **Find out the number.**

Check your answer:-

Click here to See AnswerHideWe can expand aabb as

=> 1000a + 100a + 10b + b

= 1100a + 11b = 11(100a + b)

for 11(100a +b) to be a perfect square 100a + b should be a multiple of 11 where a and b both are integers and single digit numbers.

lets say 100a + b = 11y, here y should also be a perfect square (such that 11*11*y is a perfect square), i.e. 1, 4, 9, 16, 25, 36

If you try to solve this, where a and b are single digit integers and y is also a perfect square, you can see one possible values of a and b are 7 and 4, where y = 64.

Thus the number should be 7744, it is a perfect square of 88.

Kids Math Puzzles #2

**What numbers should replace question marks ??**

Check your answer:-

**First Column**

**Second Column**

All the rivers are magical, moment a worshiper crosses a river with any number of flowers, it becomes double. (For eg 1 flower becomes 2 flowers, 2 become 4 and so on).

**How many minimum number of flowers** a worshiper needs 2 carry from beginning such that he offers equal number of flowers in all the three temples, and he is left with zero flowers at the end of fourth river.

**Solve this ??**

Check your answer:-

Click here to See SolutionHide

Lets assume that he offers x flowers at every temple, thus he must have only x flowers left at the end of 3rd temple, otherwise he will not have zero flowers at the end of fourth river.

also we can say that after offering flowers at second temple he should be left with x/2 flowers.

similarly after offering flowers at first temple he should be left with (3x/2)/2 flowers.

Thus he should be carrying (x + 3x/4)/2 flowers initially, i.e. 7x/8 flowers initially.

For number of flowers to be integer, x =8, thus he must carry 7 flowers initially and offer 8 flowers at each temple.

Solve this

0 0 0=6

1 1 1 = 6

2 2 2=6

3 3 3 =6

4 4 4=6

5 5 5=6

6 6 6=6

7 7 7=6

8 8 8=6

9 9 9=6

In the space you can use any kind of functions like addition subtraction divison etc

But you cannot bring up new numbers

Eg: 2+2+2=6

Check your answer:-

Click here to See Answer with explanationHide

Here as there are no braces, operators will work as per their precedence.

division and multiplication has same precedence and addition and subtraction has same precedence. Also / and * has higher precedence then + and -.

Thus first % and * should operate, now they being of the same precedence, they will work from left to right order thus % will operate first and the * will work on its result.

division and multiplication has same precedence and addition and subtraction has same precedence. Also / and * has higher precedence then + and -.

Thus first % and * should operate, now they being of the same precedence, they will work from left to right order thus % will operate first and the * will work on its result.

Thus 36%6*3 -9 +1 => 6*3 -9 +1 => 18 -9 + 1=> 10

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