All my digits are non-zero perfect squares. If you treat my first two digits as a two-digit number, and treat my last two digits as a two-digit number, the sum of these two numbers is also a perfect square. If I am a three digit number, what numbers could I be?

In the addition problem below, some digits are missing. They have been replaced by x and y. Find the values of x and y.

3xy2 + 3y1 = 40x3

When Shrek asks Fiona for her telephone number, Fiona is a bit coy about it, and tells Shrek the following information:

• My telephone number has 10 digits.
• There are no repeated digits in my telephone number.
• The first three digits are in ascending order.
• The second three digits are in descending order.
• Both the last four digits and the last two digits are multiples of sixty.
• My last four digits are not a multiple of 43.
• My first three digits are the square of an integer less than twenty.
• The sum of the second three digits is 14.

What number should Shrek dial?

I am a four digit number.

The sum of my digits is 20.

The product of my digits is 600.

The difference between my first two digits is 2, and the sum of my middle two digits is 11.

What number am I?

Happy New Year! I am a four-digit year, and my last two digits are a perfect square. The sum of my first and third digits is a perfect square. My second digit is a perfect square. All my digits add to a perfect square.

If you subtract my first, second, and third digit from my last digit, you get a perfect square.

If you subtract my third digit from my first digit, you get a perfect square.

Oh, by the way, I'm a perfect square.

What year am I?

How many two-digit numbers are there such that the digits match at least one of the following patterns:

1. The digits are both multiples of three.
2. Neither of the digits are multiples of two.
3. The digits add to 8.
4. The digits are perfect squares.