Substituting the four numbers 1, 9, 8 and 3, for the four letters in the addition problems (different number for different letters) BAD + MAD + DAM. Find the largest sum!
this is not hard. Just start listing the sums:
ABDM
1983: 918+318+813=2049
...
There are only 24 ways to arrange the numbers. Crank it out. I think you can eliminate all the ones where A is not 1. That makes one of the other leading letters be 1; not a likely choice.
I found one that's two bigger.
819+319+913=2051
I found one that's 5 bigger than what which I'm good at found.
B=3
A=1
D=9
M=8
319+819=1138
1138+918=2056
Go me!
To find the largest sum when substituting the numbers 1, 9, 8, and 3 for the letters in the addition problem BAD + MAD + DAM, we can try different combinations and calculate the sums.
Let's start by assigning the value 9 to letter B, 8 to A, 3 to D, and 1 to M:
9 8 3 +
1 9 8 +
3 8 9
------
? ? ?
Now, we can calculate the sum by adding the numbers vertically, starting from the rightmost column:
3 + 8 + 9 = 20. Write down 0, carry over 2.
1 + 9 + 8 + 2 = 20. Write down 0, carry over 2.
9 + 8 + 3 + 2 = 22. Write down 2.
So, the sum is currently 220.
To find a larger sum, we need to rearrange the numbers among the letters. Let's try assigning the value 9 to letter B, 8 to A, 1 to D, and 3 to M:
9 8 1 +
1 9 8 +
3 8 9
------
? ? ?
Performing the vertical addition again:
1 + 8 + 9 = 18. Write down 8, carry over 1.
1 + 9 + 8 + 1 = 19. Write down 9, carry over 1.
9 + 8 + 1 + 1 = 19. Write down 9.
The sum is currently 998.
Thus, the largest sum we obtained is 998, which occurs when the letters B, A, D, and M are represented by the numbers 9, 8, 1, and 3, respectively.