They are 2, 3, and 6.
As to how, the product being 36 means they are either 2,2,9 or 3,3,4 or 2,3,6. The total being the apt number rules out 2,2,9 because it adds to 13 (not really - there are apt #13s in the world - but that's the only reason I can think of that this clue would be included; would have been better as a clue about the floor number they lived on). Of the remaining possibilities, only 2,3,6 has an oldest to have red hair (again not really as one of the twins would be older than the other and they could be fraternal so only the oldest is red-headed, but that's what the clue intended). Thus 2,3,6 wins.
Edited By TPRJones on 1434624213
Riddle
It's actually 9, 2, 2. TPR's on crack.
Step 1: Come up with all the ways to make 36. Here's what I came up with:
Age1 Age2 Age3 Mult Sum
1 1 36 36 38
2 1 18 36 21
4 1 9 36 14
2 2 9 36 13
3 1 12 36 16
6 1 6 36 13
2 3 6 36 11
3 3 4 36 10
Step 2: Look at the Sums of all the ages. Notice that they are all distinct, EXCEPT the two sets that add to 13. Thus, if the person could not figure it out from this clue, the ages must add to 13, since that's the only sum that is repeated and non-distinct. Therefore, only 2-2-9 and 6-6-1 are valid possibilities.
Step 3: Oldest has red hair means that there is a SINGLE oldest, so it cannot be 6-6-1. (Realistically, it could be, like one could be 6 yrs 11 months, and the other 6 years 1 month or such, but for simplicity, let's assume that the same year = twins).
Therefore, it's 2-2-9
Edited By TheCatt on 1434633294
Step 1: Come up with all the ways to make 36. Here's what I came up with:
Age1 Age2 Age3 Mult Sum
1 1 36 36 38
2 1 18 36 21
4 1 9 36 14
2 2 9 36 13
3 1 12 36 16
6 1 6 36 13
2 3 6 36 11
3 3 4 36 10
Step 2: Look at the Sums of all the ages. Notice that they are all distinct, EXCEPT the two sets that add to 13. Thus, if the person could not figure it out from this clue, the ages must add to 13, since that's the only sum that is repeated and non-distinct. Therefore, only 2-2-9 and 6-6-1 are valid possibilities.
Step 3: Oldest has red hair means that there is a SINGLE oldest, so it cannot be 6-6-1. (Realistically, it could be, like one could be 6 yrs 11 months, and the other 6 years 1 month or such, but for simplicity, let's assume that the same year = twins).
Therefore, it's 2-2-9
Edited By TheCatt on 1434633294
It's not me, it's someone else.
It means there's no ginger twin of the oldest running around. It's very much a recessive gene thing. Any number of traits have that property.
Edited By Malcolm on 1434644880
Edited By Malcolm on 1434644880
Diogenes of Sinope: "It is not that I am mad, it is only that my head is different from yours."
Arnold Judas Rimmer, BSC, SSC: "Better dead than smeg."
Arnold Judas Rimmer, BSC, SSC: "Better dead than smeg."
TheCatt wrote:TPR's on crack.
I completely forgot to include 1 as a valid age and divisor of 36, which completely changes the tone and meaning. I like your version better (that 13 thing I used as a clue seemed a bit weird).
EDIT: That last clue is still a little messy, though. It could be 6 6 1 with one 6 being born in January with red hair (the older) and one born in November with brown hair (the younger). The 6s don't have to be twins. Not a logical necessity that it makes it 2 2 9, just makes it more likely.
Edited By TPRJones on 1434645518
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Wouldn't change the riddle. The logician said "has red hair." If there were a capillum-melanin identity disorder involved the logician may have said "is red-headed" to acknowledge the child's choices, but no logician would go so far as to actually say "has red hair" in that case because that would be technically inaccurate.
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