Likewise (but a different solution) if D said “the sum of my cards is equal to the product of someone else’s cards.”

]]>Re the comment above, echo adds a newline by default, you get the expected hash with `echo -n “$a,b,$c” | md5sum`.

]]>Blaine, I have checked all the possibilities and none of them has that MD5 hash. Using this (plus trying adding newlines and similar):

“`bash

for a in $(seq 10)

do

for b in $(seq $a 11)

do

for c in $(seq $b 12)

do

suma=$(echo “$a,$b,$c” | md5sum)

echo $a,$b,$c,$suma

done

done

done

“`

Hint 2: 1 is neither prime nor composite. If D has 1, can he deduce the numbers of A and C. So who has 1?

Hint 3: C could have {6,9,12} or three cards from {4,6,10,12}. D is able to conclusively eliminate one of these cases. That wouldn’t happen if D had 4 or 10. Would that happen if D had 9? Remember C could have any 3 of the 4 numbers in {4,6,10,12}. So what numbers remain as possible ones held by D? And what does that tell you about 9?

Hint 4: Does the question ask you for the specific cards of B,C or D? Do you need to know them?

]]>