Sum, difference and equality puzzle

  • Context: Undergrad 
  • Thread starter Thread starter K Sengupta
  • Start date Start date
  • Tags Tags
    Difference Puzzle Sum
Click For Summary
SUMMARY

The discussion focuses on solving a cryptarithmetic puzzle involving the equation GEORGE + RUGGLE + 15750 + 16220 + P = PPPPPP. Key insights include that RUGGLE must be a six-digit number divisible by both 7 and 5, leading to the conclusion that it is a multiple of 35. The analysis reveals that E must be either 0 or 5, and the relationship OE - LR = LO provides a formula for calculating O based on L and R. The final solution is reached by enumerating possible values for RUGGLE and verifying the conditions.

PREREQUISITES
  • Understanding of cryptarithmetic puzzles
  • Basic knowledge of modular arithmetic
  • Familiarity with divisibility rules, particularly for 5 and 7
  • Ability to perform systematic enumeration of possibilities
NEXT STEPS
  • Explore advanced techniques in solving cryptarithmetic puzzles
  • Learn about modular arithmetic applications in problem-solving
  • Investigate divisibility rules for larger sets of numbers
  • Study algorithms for systematic enumeration and constraint satisfaction problems
USEFUL FOR

Mathematicians, puzzle enthusiasts, educators teaching problem-solving techniques, and anyone interested in cryptarithmetic challenges.

K Sengupta
Messages
113
Reaction score
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
 
Mathematics news on Phys.org
E=0 I think
 
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
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 1 ·
Replies
1
Views
4K