Welcome 2016! Part 33
+ 1 7 8 2 4 2 1 2 9 2 5 4 0 8 3 1 6 0 6
Obviously, the above addition is incorrect.
However, the display can be corrected simply by changing one digit d , wherever it occurs, to another digit e . Find the value of d + e .
The answer is 8.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
4 solutions
But then how does the last column work? 1+7+8=16
6 + 0 =6 8 + 3 =11 5 + 4 + 1=10 2 + 9 + 1=12 4 + 6 + 1 =11 7 + 8 + 1 = 16 doesnt work as the amswer says 12
Log in to reply
You have to change all 2's to 6's, even the 2's in the sum. So that 12 becomes a 16.
Log in to reply
OMG, this is so unintuitive, I thought I had to change only one-digit like one number not treat numbers as variables cause that's weird, I even wrote a program to check for every number changing to every number proving it's impossible to change just one number.
Can't you also change 8 and 4?
Log in to reply
No. Note that the problem says "changing one digit d , wherever it occurs, to another digit e . " This is not the same as swapping two numbers.
However, the fact that the 4 and the 8 can be swapped is an interesting observation!
I agree with switching the 4 and the 8. 782586 + 429430 = 1212016.
We couldn't change 4 and 8 because then the second or tens column would be 4 + 3 = 1 which doesn't work
we could also change 8,4 then the sum would be 8+4=12
Log in to reply
the problem is all about changing a single number instead of switching between two numbers' positions. Be careful, although I thought that was also a good answer too
OMG, this is so unintuitive, I thought I had to change only one-digit like one number not treat numbers as variables cause that's weird, I even wrote a program to check for every number changing to every number proving it's impossible to change just one number.
4 + 2 cannot lead to 1 with or without a carry. Therefore, the wrong digit is 1, 2 or 4.
7 + 8 cannot lead to 2 with or without a carry. Therefore, the wrong digit is 2, 7 or 8.
The only digit in common to these two sets is 2. Therefore the wrong digit is 2. By replacing 2 with an unknown, a simple linear equation leads to 6 as the missing digit.
The problem goes wrong when it reaches the 3rd column.
So it is either 4, 2 or 1.
We see that we cannot change 4 or 1 since it will make the previous columns incorrect. And we figure that changing 2 to 6 is the solution.
| 7 | 4 | 2 | 5 | 8 | 6 | ||
| + | 8 | 2 | 9 | 4 | 3 | 0 | |
| 1 | 2 | 1 | 2 | 0 | 1 | 6 | |
| x | x |
by changing one digit d
The only digit appears in both incorrect columns is 2.
7+8+1 = 16, so change 2 to 6.
As we can see, this line is the first issue we reach so either 4, 2 or 1 must be changed. We can also see that in the line before (2+9+1=12) since the units digit of the answer and the first digit to be added is the same, changing this number will not affect the sum. As such we change 2 to 6 to fix the broken line as such: 4+6+1 = 11 This works for all columns of the equation and so the answer is 2 + 6 = 8