# Perfect Square Puzzles

**Squaring Puzzles- **Find below 2 interesting puzzles related to square of some number. Hope you will like them.

### Puzzle 1

The square of 13 is 169. Take the last digit of the square, 9, and place it in the middle, making 196. This is the square of 14, the next number above 13.

What are the next numbers which also have this property?

### Puzzle 2

The following multiplication example uses every digit from 0 to 9 at least once. Letters have been substituted for the digits. Can you replace the letters and make the original multiplication problem?

B O G

x B O G

_______________

L Y L E

G G U L

T U O O

___________________

U N I T O E

8 Comments

sir your puxxles are outstanding

Square of 15=225,last digit is 5.

which is middle number of successive digit square i.e16 square = 256

superb tricks used plz upload sum more

amazing

12 square is 144

21 square is 441

By interchanging number we get a new puzzle.

yet another :

13 square is 169

31 square is 961.

12 square is 144

21 square is 441

By interchanging number we get a new puzzle.

13 is the only number with property that it’s square and that of it’s successor concide after interchanging last 2 digits of square of latter.

int ten(int x)

{

if(x<10)

return x;

else

{

x = x/10;

x =x%10;

return x;

}

}

int zero(int x)

{

return (x%10);

}

int newnum(int x)

{

x=10*ten(x)+zero(x);

return x;

}

int rev(int x)

{

int s = 0;

s+=10*(x%10);

x=x/10;

s+=x;

return s;

}

int anoop(int x)

{

int i;

i = x/100;

return (i*100 + rev(x%100));

}

int main(void)

{

int x,limit,y,z;

printf("INPUT A LIMIT");

scanf("%d",&limit);

for(x=10;x<=limit;x++)

{

if((x*x)-anoop((x+1)*(x+1))==0)

printf("%d\n",x);

}

getch();

return 0;

}

Hi Anoop,

Great efforts!!

but I think u have slightly misunderstood the problem… when u r saying – “….after interchanging last 2 digits of square of latter.”

Actually it’s the middle digit which is replacing the last digit. So if the square is a 5 digit number, the hundred’s digit is replaced by unit’s digit.

I hope now you will get the answer!