Sum, difference and equality puzzle

[K Sengupta]

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

 

[brother time]

E=0 I think

 

[I like Serena]

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.

Spoiler

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