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

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

8 thoughts to “Perfect Square Puzzles”

  1. Square of 15=225,last digit is 5.
    which is middle number of successive digit square i.e16 square = 256

  2. 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.

  3. 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;

    }

    1. 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!

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