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Go 2 Gig, Get Minimum (Posted on 2007-05-25) Difficulty: 3 of 5
Minimize the bases P and Q such that each of the following alphanumeric equations has at least one solution:

(A) (GO)Base P + (GO)Base P = (GIG)Base P

(B) (GO)Base Q*(GO)Base Q = (GIG)Base Q

Note: Solve each of the alphanumeric equations separately and remember G, O and I must be distinct and G can't be zero.

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Analytical Soltuion (more solutions) Comment 3 of 3 |
(In reply to Analytical Soltuion by Gamer)

It is clear that prime Q (like 7) are not possible. However for other Q>7, there still may be solutions.

The goal is for there to be a multiple of Q in the form O^2-1 less than Q(Q-5).

Since O^2-1=(O+1)(O-1) it can be seen that we need some of the factors from Q to come from (O+1) and some to come from (O-1), but the remaining factors' product needs to be less than (Q-5). So looking for numbers of the form O^2-1 and their large factors gives a list for O and Q. From this, I can be computed and the solution determined.

  Posted by Gamer on 2007-05-25 23:41:17

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