1. Find a set of three different whole numbers whose sum is equal to their total when multiplied.

2. What is the smallest whole number that is equal to seven times the sum of its digits?

3. What is the smallest number that increases by 12 when it is flipped and turned upside down?

Have fun!

BlackjackEd Sep 13, 2023

#3**+1 **

Let's tackle each of these questions one by one:

1. Find a set of three different whole numbers whose sum is equal to their total when multiplied.

One such set of three different whole numbers that satisfy this condition is **{2, 2, 3}**.

- The sum of the numbers: 2 + 2 + 3 = 6

- The product of the numbers: 2 x 2 x 3 = 6

As you can see, the sum (6) is equal to the product (6).

2. What is the smallest whole number that is equal to seven times the sum of its digits?

Let's call the two digits of this number 'a' and 'b'. The number can be represented as 10a + b. According to the given condition, this number should be equal to seven times the sum of its digits, which is 7(a + b).

Therefore, we have the equation:

10a + b = 7(a + b)

Let's simplify this equation:

10a + b = 7a + 7b

Now, subtract 7a from both sides of the equation:

3a + b = 7b

Next, subtract b from both sides:

3a = 6b

Divide both sides by 3:

a = 3b

So, the smallest whole number that satisfies this condition has two digits: one digit is 3 times the other digit. The smallest such number is **31**.

3. What is the smallest number that increases by 12 when it is flipped and turned upside down?

A number that remains the same when flipped and turned upside down is a "palindromic number." To find the smallest such number that increases by 12 when flipped, let's start by considering two-digit palindromic numbers. We can write them in the form of 'ABA,' where A and B represent digits.

The smallest two-digit palindromic number is 11. When we flip and turn it upside down, it remains 11, which is not increased by 12.

Let's consider the next two-digit palindromic number, 22. When flipped and turned upside down, it remains 22, which is also not increased by 12.

Let's continue this pattern until we find a palindromic number that increases by 12 when flipped.

The next two-digit palindromic number is 33, and when we flip and turn it upside down, it becomes 33 + 12 = 45. So, the smallest number that increases by 12 when flipped and turned upside down is **33**.

SpectraSynth Sep 13, 2023

#7**-2 **

To find the smallest whole number that is equal to seven times the sum of its digits, we can start by considering the smallest possible number, which is 1.

Let's calculate the sum of the digits of 1: 1 = 1.

Now, let's check if this number satisfies the condition of being equal to seven times the sum of its digits: 7 * 1 = 7.

Since 7 is not equal to 1, we need to try the next smallest number, which is 2.

The sum of the digits of 2 is: 2 = 2.

Now, let's check if this number satisfies the condition: 7 * 2 = 14.

Since 14 is not equal to 2, we continue to the next number.

We repeat this process for each subsequent number until we find the smallest whole number that satisfies the condition.

After trying a few more numbers, we find that the smallest whole number that is equal to seven times the sum of its digits is 7.

The sum of the digits of 7 is: 7 = 7.

And, 7 * 7 = 49, which is equal to 7.

Therefore, the smallest whole number that is equal to seven times the sum of its digits is 7.

taylorgodiva28 Sep 14, 2023

#8**0 **

Hmmmm.... I dunno.... to ME digit__ s__ is plural...as in more than one digit....

others may read this as you did which would make your answer correct....

So....this question is subject to interprotation.... making it a poorly worded problem !

ElectricPavlov
Sep 14, 2023