Each letter in this addition problem stands for a different digit, but every letter stands for the same digit everywhere it appears. For example, all of the C's stand for the same digit.
and the question is ... ?
Each letter in the following addition problem
represents a different digit and each of the same
letter represents the same digit. No letter can be
either 5 or 9.
Determine the sum PLAN in this cryptarithm.
Directions to Students: After all questions have been read by your PICO, you will have 30 minutes to complete this contest. You may
not have a pen or pencil in your hand while the PICO reads the set of questions to the class. Calculators are not permitted. All work is
to be done on the pages provided. No additional scrap paper is to be used. Answers must be placed in the corresponding boxes in the
answer column.
5 A 9
5 A 9
+ 5 A 9
PLAN
It seems that you have described a cryptarithm or alphametic puzzle. Unfortunately, you have not provided the specific addition problem for me to solve. Could you please provide the addition problem with the corresponding letters?
To solve this type of addition problem where each letter represents a different digit, we can use a process called algebraic substitution.
Let's represent each letter with a different variable to make it easier to work with. For example, let's use A, B, C, etc. to represent the digits that the letters stand for.
Now, let's break down the addition problem and assign variables to each letter. For example, if the addition problem is:
ABCD
+ ABCD
--------
EFGHI
We can assign variables as follows:
A B C D
+ A B C D
--------------
E F G H I
Since each letter represents the same digit everywhere it appears, we have:
A B C D
+ A B C D
--------------
E F G H I
Now, let's solve the problem step by step:
First, let's focus on the rightmost column, which is column D. If we add the two D's together, we get 2D. Since D represents a single digit, it means 2D must equal some two-digit number, which is not possible. Therefore, we cannot directly determine the value of D from this column.
Moving on, let's look at the column to the left of D, which is column C. Adding the two C's together gives us 2C, but we also need to add any carryover from the rightmost column. Since D represents some digit and 2D is not a two-digit number, it means there is no carryover to the C's column. Therefore, C + C equals 2C. We know that each letter stands for a different digit, so C cannot be zero. Therefore, C must be 1.
Now, we have:
A B 1 D
+ A B 1 D
---------------
E F G H I
Next, let's move to the column to the left of C, which is column B. Adding the two B's together gives us 2B, but we also need to add any carryover from the C's column. Since C is equal to 1, there is no carryover to the B's column. Therefore, B + B equals 2B. Again, since each letter represents a different digit, B cannot be zero. Therefore, B must be 1.
Now, we have:
A 1 1 D
+ A 1 1 D
---------------
E F G H I
Moving further to the left, we come to column A. Adding the two A's together gives us 2A, but we also need to add any carryover from the B's column. Since B is equal to 1, there is no carryover to the A's column. Therefore, A + A equals 2A. Again, since each letter represents a different digit, A cannot be zero. Therefore, A must be 1.
Now, we have:
1 1 1 D
+ 1 1 1 D
---------------
E F G H I
Finally, let's look at the leftmost column, which is column E. Adding the two 1's together gives us 2, but we also need to add any carryover from the A's column. Since A is equal to 1, there is no carryover to the E's column. Therefore, E must be 2.
Now, we have:
1 1 1 D
+ 1 1 1 D
---------------
2 F G H I
To find the remaining digits F, G, H, and I, we would need additional information or equations. Without any additional information, we cannot determine the values of these digits.