Set of Five Digit Numbers

Pro Problems > Math > Number and Quantity > Number Theory > Digits

Set of Five Digit Numbers

S is the set of five-digit numbers such that the digits are in ascending order, there are no repeated digits, the sum of the first two digits is equal to the third digit, and the sum of the third and fourth digits is equal to the two more than the fifth digit. How many elements are in the set S? (Note that the leading digit cannot be a zero).

Presentation mode

Problem by Mr. Twitchell

Solution

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.

Assign this problem

Click here to assign this problem to your students.

Similar Problems

Digits in a Multiplication Problem

You must use each of the integers from 0 to 5 exactly once to fill in the blanks in the multiplication problem below.

_ _ _ x _ _ x _ =

What is the largest possible value you can create?

Two Digit Pattern Matching

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

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

Five Digit Number

The sum of the digits of a three digit number is eighteen. The first digit is three more than the last digit. There is a repeated digit in the number. What are all possible values of the number?

Fiona's Telephone Number

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?

Three Digit Number

I'm thinking of a three-digit number. The sum of its digits is between 15 and 20 exclusive. The product of my first and last digits is 18. I don't have any repeated digits, and my digits are not in either ascending order or descending order. I am a multiple of three, but not of six. What number am I?

Fill in the blanks

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

Happy New Year

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?