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Topic: 1-10 and Aa to Ee (Read 369 times) |
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Noke Lieu
Uberpuzzler
pen... paper... let's go! (and bit of plastic)
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1-10 and Aa to Ee
« on: Dec 2nd, 2007, 5:47pm » |
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another one of these little things. A bit rusty, slightly ill... apologies if it's not up to muster.
As a recap: two of the numbers 1-10 are allocated a letter, either a or A.
(a<A... n<N you get the picture)
Whilst all the totals (a+A etc) are 5n, only one is 3n
c and C are prime
b is factor of B
a is even
cb = D
what are they?
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| « Last Edit: Dec 5th, 2007, 2:40pm by Noke Lieu » |
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a shade of wit and the art of farce.
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FiBsTeR
Senior Riddler
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Re: 1-10 and Aa to Ee
« Reply #1 on: Dec 2nd, 2007, 6:22pm » |
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Fun puzzle! I find:
a = 4
A = 6
b = 2
B = 8
c = 3
C = 7
d = 1
D = 9
e = 5
E = 10
Hint: Attack b and B first. Since b|B, 5|b+B, cb=D, and B>b, what are the possible pairs for (b,B)? Many values lock into place from these observations, and I found only 2 cases to consider.
I was going to put my solution in a table, but apparently they can't be hidden. 
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Joe Fendel
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Posts: 158
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Re: 1-10 and Aa to Ee
« Reply #2 on: Dec 4th, 2007, 4:30pm » |
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Cute. Actually, when I solved, I didn't even use two of the facts. That b | B, or that only one pair adds to a multiple of 3. I wonder which other combinations of information were unnecessary for the solution.
| hidden: | | c and C are primes which add to a multiple of 5. Our options are thus 2+3 or 3+7. Next we see that cb = D. Clearly b is not 1, since then c = D. If c=2 and C=3 then those values are out for b, so b > 3 which makes D > 10. Thus c=3, C=7, and cb = D can only be fulfilled with b=2 and D=9. Thus B = 8 is the only value which can be added to b to get a multiple of 5. Next use the fact that a is even, but it is not 2 or 8 (already used) or 10 (too big). If a=6, then the only number larger which adds to a multiple of 5 is A=9, but this can't be because D=9. Thus a=4, and so A=6 (because 1 is too small). We're then left with 1 as the only option for d which can add to 9 to get a multple of 5, and so d=1, and conclude that e=5 and E=10. |
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| « Last Edit: Dec 4th, 2007, 4:32pm by Joe Fendel » |
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Noke Lieu
Uberpuzzler
pen... paper... let's go! (and bit of plastic)
Gender:
Posts: 1884
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Re: 1-10 and Aa to Ee
« Reply #3 on: Dec 5th, 2007, 2:37pm » |
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yup.
Minimum number of clues is a mystery for me.
I realised that the c^b=D was a hugely powerful clue, but like I say- a little rusty at puzzling. And about to beachward.
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