. Below, the standard addition algorithm is being used to add three two-digit numbers.
4z
27
+x5
y14
If x, y and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)?
answer is 8.
2*4*1=8
z+7+5=4 or 14, so z=2
4+2+x+1 (from carry)=1 or 11, so x=4
0+0+1 (from carry) =y so y=1
x=4, y=1, z=2
What is xyz?
114
Well, let's solve this math puzzle with a bit of humor, shall we? Now, as an esteemed Clown Bot, I would like to point out that I am really good at juggling numbers, and in this case, I'll be juggling digits.
Now, looking at the hundreds place, we only have one digit, so there's no carrying involved. In the tens place, we have z + 2 + 5 + 1 = 8 + z. Since this must be a two-digit number, z has to be 2.
Now, looking at the ones place, we have 4 + 7 + x + 5 = 1 + y. Simplifying it a bit, we get (x + 16) = (y - 1). Now, since x and y cannot be the same, let's start juggling some numbers.
We know that x needs to be greater than 1 for the equation to be valid. Let's start by assigning x as 8 and y as 2. That gives us (8 + 16) = (2 - 1), or 24 = 12, which is incorrect.
Let's try another combo! This time, let's assign x as 3 and y as 7. That gives us (3 + 16) = (7 - 1), or 19 = 6, which is also incorrect. Oh no! Clown Bot is dropping the numbers!
Okay, let's give it one more shot. This time, let's assign x as 9 and y as 3. That gives us (9 + 16) = (3 - 1), or 25 = 2, which is definitely incorrect. Uh-oh, Clown Bot is really struggling now!
After juggling through all these possibilities, it seems that there is no combination of x, y, and z that will make this equation work. So, unfortunately, we cannot find the value of (x)(y)(z). No laughter here, just some mathematical hiccups for Clown Bot.
To find the value of (x)(y)(z), we need to solve the addition problem using the standard addition algorithm and then find the values of x, y, and z.
Let's start by adding the digits in the rightmost column: z + 7 + 5 = 14. The digit 4 is represented in the result, and the 1 is carried over to the next column.
Now, let's move to the next column and add the digits: z + 2 + 1 = z + 3. Since the sum is a two-digit number, we need to carry over another digit to the next column.
Finally, in the leftmost column, we have 4 + 1 + y = 5. Therefore, y = 5 - 4 - 1 = 0.
Now, let's examine the second column from the left. We have x + 2 + 0 = z + 3. Since z + 3 is composed of two digits, we know that x + 2 must be equal to z + 13. Therefore, z + 13 - 2 = x.
Looking at the rightmost column again, we have z + 7 + 5 = 14. Since y = 0 and z + 7 = 14, we can deduce that z = 7.
Now, we can substitute the values that we found into the equation (x)(y)(z). Therefore, (x)(y)(z) = (7)(0)(7) = 0.