On that AB = 'product of first six primes', A+B = composite, A-B = composite.
I was unable to get any analytical insight going, but found these solutions
quickly enough by hand - A=3003, B =10 or A=1365, B=22.
Unfortunately, because my method was by brute force I had to check all the
rest of the possibilities in order to ensure there were not still more...
and THAT was a drag.
Brooke Dane
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Hi, Ed; I see there's no answer to your June 3rd puzzle:
(unless you forgot to put 'em up)
>A small puzzle: A B = product of first six primes.
>A+B = composite. A-B = composite. What are A & B ?
There are 2 solutions:
A = 10, B = 3003 (3013 and 2993, both composite)
A = 22, B = 1365 (1387 and 1343, both composite)
In case you'd like to add a bit of challenge to
June 3rd, here's a similar but more complicated one:
A B C D = product of first six primes. A>B>C>D>1.
X = A+B+C+D = composite. Y = A-B+C-D = composite.
What are A & B & C & D ?
There are 14 cases: find the 2 with same X and same Y.
Answer:
A B C D X Y
33 14 13 5 65 27
35 13 11 6 65 27
Denis Borris Ottawa Ontario Canada.
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> A small puzzle: A B = product of first six primes.
> A+B = composite. A-B = composite. What are A & B?
Brute force search yielded 2 solutions:
Solution 1:
A = 1365 = 3*5*7*13 B = 22 = 2*11
A+B = 1387 = 19*72 A-B = 1343 = 17*79
Solution 2:
A = 3003 = 3*7*11*13 B = 10 = 2*5
A+B = 3013 = 23*131 A-B = 2993 = 41*73
--
Stephen Kloder
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a = 3 * 7 * 11 * 13 = 3003
b = 2 * 5 = 10
ab = 2 * 3 * 5 * 7 * 11 * 13
a + b = 3013 = 23 * 131
a - b = 2993 = 41 * 73
--
James Deikun, Techie(tm), CSI Multimedia
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In addition to A=3003 and B=10, the only other solution to
A>B, A*B=2*3*5*7*11*13, with both A+B and A-B being composite
is A=1365 and B=22. (1365+22=1387=19*73 and 1365-22=1343=17*79)
Al Stanger
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Ed,
There are two solutions to the first six primes puzzle.
A + B A - B
3013 2993
1387 1343
Dick Saunders Jr.
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If A=3003 and B=10, then
(i) A*B=30030=2*3*5*7*11*13
(ii) A+B=3013=23*131
(iii) A-B=2993=41*73
Al Stanger
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S T U T T E R #
I E T I E S # P
E N N A S # S I
N S I L # U T E
N I K # S P U T
A L # T E R T I
S # S E M I T E
# U P R I S E S
I started with stammer, ?, siennas, ?, sputnik,
tertial (Googled), Semites, ?. Couldn't make it
work. Then tried 'stutter'. The possible
intersections with other words were all, ?, SE,
?, STU, ERT, EST, all. I tried intersecting
stutter/sputnik at U and the rest followed
quickly. It's like some variety cryptics in that
you can't write anything down until you have
several answers (at least three, I think), so
it needs reasonably transparent clueing. Given
that, I like the idea.
Acag, Treesong
----------------------------------------------------
Given this answer:
R-STUTTE
-PIETIES
SIENNAS-
TENSIL-U
UTNIK-SP
TIAL-TER
TES-SEMI
ES-UPRIS
The downs are in the SAME order as the acrosses.
--Philana