Sum, difference and equality puzzle

In summary, the goal of this conversation is to find the values of each letter (represented by a digit from 0 to 9) in the equation GEORGE + RUGGLE + 15750 + 16220 + P = PPPPPP, while satisfying the conditions OE - LR = LO, E + E + P -> P, and RUGGLE being a multiple of both 7 and 5. After analyzing the equation and the given conditions, it is determined that E must be either 0 or 5 and RUGGLE must be a multiple of 35. The lowest possible value for RUGGLE is 123375 and the highest is 987735. Additionally, O can be calculated using the formula (
  • #1
K Sengupta
113
0
Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero.

GEORGE + RUGGLE + 15750 + 16220 + P = PPPPPP, and:

OE - LR = LO, and:

RUGGLE is divisible by 7
 
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  • #2
E=0 I think
 
  • #3
Since E + E + P -> P, E must be either 0 or 5, so E is a multiple of 5.

RUGGLE is a multiple of 7 and a multiple of 5, so ruggle is a multiple of 35.

With RUGGLE being 6 digits and R nonzero, that means that the lowest value for RUGGLE is 123375 and the highest 987735.

With OE - LR = LO it follows that O = (20 x L + R - E) / 9

Looking at the 5th digit of the sum it follows that:
P = (G + L + 5 + 2 + 2 x E / 10) mod 10

Now we can simply enumerate all possible values of RUGGLE, calculate O and P and check if the conditions are met.
Finally only 1 answer remains.

george + ruggle + 15750 + 16220 + p = pppppp oe - lr = lo
609160 + 136640 + ... + ... + 7 = 777777 90 - 41 = 49
 

1. What is a "sum, difference and equality puzzle"?

A sum, difference and equality puzzle is a type of mathematical problem where the goal is to find the values of two or more variables that satisfy a given set of equations or inequalities.

2. How do I solve a "sum, difference and equality puzzle"?

To solve a sum, difference and equality puzzle, you can use algebraic methods such as substitution, elimination, or graphing to find the values of the variables that satisfy the given equations or inequalities.

3. What are some tips for solving "sum, difference and equality puzzles"?

Some helpful tips for solving sum, difference and equality puzzles include: identifying the unknown variables and assigning them variables, setting up equations or inequalities based on the given information, and using logical reasoning to eliminate potential solutions.

4. Are there any real-world applications for "sum, difference and equality puzzles"?

Yes, sum, difference and equality puzzles have many real-world applications, such as in engineering, economics, and physics. These types of problems are used to model and solve real-world scenarios that involve multiple variables and constraints.

5. What are some common mistakes when solving "sum, difference and equality puzzles"?

Some common mistakes when solving sum, difference and equality puzzles include: making calculation errors, not checking for extraneous solutions, and not considering all possible cases or scenarios. It is important to carefully check and verify your solutions to avoid these mistakes.

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