# Dwelling upon the triangular numbers

• K Sengupta
In summary, triangular numbers are a sequence of numbers that form a triangle when arranged in rows. They are found by adding consecutive natural numbers, starting from 1. To calculate the nth triangular number, you can use the formula n(n+1)/2. Triangular numbers have many applications in mathematics and science and cannot be negative. There are infinitely many triangular numbers.
K Sengupta
Each of Hank, Jim and Larry chose a different five-digit triangular number whose digits had the pattern DWELL, where each different letter represents a different base-10 digit. Jim's triangular number had no digit in common with either Hank's or Larry's.

Determine the numbers chosen by each of the three individuals.

Note: None of the numbers can contain any leading zero.

There are two solutions
Jim = 27966
Hank = 15400
Larry = 58311

-and-

Jim = 27966
Hank = 58311
Larry = 15400
I used brute force to solve this.

jimmy, you've been brutal today.

## 1. What are triangular numbers?

Triangular numbers are a sequence of numbers that form a triangle when arranged in rows. They are found by adding consecutive natural numbers, starting from 1.

## 2. How do you calculate triangular numbers?

To calculate the nth triangular number, you can use the formula n(n+1)/2. For example, the 5th triangular number would be 5(5+1)/2 = 15.

## 3. What is the significance of triangular numbers?

Triangular numbers have many applications in mathematics and science, including in geometry, algebra, and number theory. They also have connections to other mathematical concepts, such as Pascal's triangle and the Fibonacci sequence.

## 4. Can triangular numbers be negative?

No, triangular numbers are defined as the sum of positive natural numbers, so they cannot be negative.

## 5. How many triangular numbers are there?

There are infinitely many triangular numbers, as you can keep adding consecutive numbers to create larger triangular numbers.

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