In the following addition problem, the numbers have been encrypted by letters. Each letter should represent a different digit (in the range from 0 to 9), and the leading digit of each number must not be zero. Determine the value of each letter so the addition works correctly. There is only one solution. KID + KID ----- DICE
In the following addition problem, the numbers have been encrypted by letters. Each letter should represent a different digit (in the range from 0 to 9), and the leading digit of each number must not be zero. Determine the value of each letter so the addition works correctly. There is only one solution.
KID
+ KID
-----
DICE
- Observe the arrangement of the letters, and state at least three facts that allow you to narrow down the possible digits that could be assigned for a letter. For this part, you do not need to give a specific value for every letter, but just state why some range of digits is required or why some digits can be ruled out for a letter. This reduces the number of possible values that need to be considered for that letter.
- Use the observations from part (a) to determine possible values for the remaining letters.
You should be able find the solution by trying possible values for each remaining letter, and then ruling out any values that do not lead to a consistent assignment of values for all letters. You may find it useful to check the addition with possible values using pencil and paper, and then enter your final values for each letter here.
(1) Observations:
(a) Since 'KID' is a three-digit number, and 'KID' + 'KID' is a four digit number, then the starting digit of the resulting sum (four digit number) can only be 1.
As Three digit number + three digit number ≤1998.
The resulting sum is 'DICE'. Hence, 'D' is surely 1.
(b) As The sum is four digit and we are adding the same number 'KID', so the number if decrypt of 'KID' must be a number whose unit digit is D = 1 and starting digit is more than or equal to 5.
i.e., K can be 5, 6, 7, 8, or 9.
(c) Since in the process of summing 'KID'+'KID', we first sum up 'D'+'D' and get 'E', and already we have that D = 1, so E = 1+1 = 2.
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