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
 

FAQ: Sum, difference and equality puzzle

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.

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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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