what is the sum of the digits of the largest even 3 digit number which is not changed when its units and hundreds digit are interchanged

Question

Illustrate a scene of an old, mathematical puzzle set in an antique classroom. A large blackboard hosts depictions of various three-digit numbers and half-erased chalk calculations. Notably, show a large and prominent three-digit even number, where the units and the hundreds digit would be the same if interchanged. Add visual elements like a wooden desk with an old calculator and parchment papers, a dusty chalk stick resting on the chalkboard ledge, a lit candle to evoke the intellectual atmosphere. Do not include any text in this image.

what is the sum of the digits of the largest even 3 digit number which is not changed when its units and hundreds digit are interchanged

Answer 1

let the unit digit be x

let the middle digit be k
let the hundred digit be y

the original number
= 100y + 10k + x
the number reversed
= 100x + 10k + y

so 100x + 10k + y = 100y + 10k + x
99x = 99y
x = y
We sort of knew that
so it doesn't matter what we put in the middle to make it as large as possible, put in 9
but the unit digit must be even

so our number is 898
and the sum of the digits is 25

Answer 2

Super 💖💖😘💖😘💖

Answer 3

This is a very big plateform for asking any suestuon.

Answer 4

Oh, hello there! Let's solve this riddle, shall we? So the largest even 3-digit number is 998. If we swap the units and hundreds digit, it becomes 899. However, that's not the same number, so let me try another joke to distract you while I figure this out:

Why don't scientists trust atoms?

Because they make up everything!

Alright, let's focus again. If we swap the units and hundreds digit of 898, it remains the same. So the sum of the digits is: 8 + 9 + 8 = 25. Ta-da!

Answer 5

To find the largest even 3-digit number that is not changed when its units and hundreds digit are interchanged, we need to consider the possible numbers in the hundreds and tens place.

We start with the largest 3-digit number, which is 999. Since we are looking for an even number, we need to consider the even numbers less than 999. The largest even number less than 999 is 998.

Now, we need to check whether 998 remains the same when its units and hundreds digit are interchanged. If we interchange the units and hundreds digit, we get 889, which is not equal to 998.

Therefore, 998 is not a number that satisfies the conditions. We need to continue searching for another number.

The next even number less than 998 is 996. If we interchange the units and hundreds digit, we would get 669, which is not equal to 996. So, 996 is not the number we are looking for either.

We continue this process until we find the number that satisfies the conditions.

The next even number is 994. Interchanging the units and hundreds digit gives us 449, which is not equal to 994.

Next, we have 992. Interchanging the units and hundreds digit gives us 299, which is not equal to 992.

Finally, we have 990. Interchanging the units and hundreds digit gives us 099, which is equal to 99.

Since 990 is equal to 99 when the units and hundreds digit are interchanged, it satisfies the conditions.

Now, we just need to find the sum of the digits of 990.

The sum of the digits is calculated by adding each digit together.

For 990, the sum of the digits is 9 + 9 + 0 = 18.

Therefore, the sum of the digits of the largest even 3-digit number that is not changed when its units and hundreds digit are interchanged is 18.