On 3/1/08, Fred lunnon <fred.lunnon@gmail.com> wrote:
I'm afraid the bound A,B < 101 is too high: an alternative solution overlooked by the setter is A = 4, B = 61 [and I think I also know the reason he missed it].
WFL Oops --- apologies in order. In fact, the given bound is unnecessarily low: I find A,B < 219 still gives a unique solution! WFL
I get the pair 4&61 arising when A,B <123. 63*2, 62*3, 61*4, 60*5, 59*6, 58*7, 57*8,...,53*12,...,47*18,...,43*22,...,41*24,...,37*28,...,33*32 then all have ambiguous factorings. So S chirps on the 61+4. P chirps, knowing 2+122 would've stumped S, being absent from the chirp list [11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65*, 67, 71, 77, ...] of pan-ambiguous sums. But then S knows P couldn't have resolved 63*2, e.g., because 6+21 is also on the list. Likewise 6+31, 15+20, etc . --rwg * but only if A=122 is legal.
Sumit: You don't know them. Pradeep: I do now! Sumit: Likewise!
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