# Possible mistake on Page 202?

• July 12, 2017 at 8:19 pm #3156
Gavriel
Participant

Seen models—H, J, K, L, M, O, P, are placed in positions 1-7 (left-right).

Conditions:
-Exactly one model between K & L.
-Exactly 3 models bet. O & L.
-K or J in the 1st position.
-M in posit. 4.

Question 2:
If K is not first, which of the following is a complete list of positions that can be occupied by H?
a) 2
b) 2,3,5
c) 2,5,6
d) 2,6
e) 6

Having diagrammed this, I came up with 3 possibilities, 2 of which involve K not being first (premise of the question). All of these options fill the 6th turn, leaving positions 2 and 5 interchangeable for free agents (H & P). Yet, the answer in the book eliminates 5 as an option, and offers 6 as an answer choice.

I can’t figure out this game. Appreciate the help in advance!

• July 13, 2017 at 12:11 pm #3157
Mike Kim
Keymaster

Hi Gavriel — happy to try and help —

let me ask you — what were the three possibilities you came up with? (you can just write them in like so: S _ P _ _ X/Y etc.) — it’d be even more helpful if you write out the process of how you got those possibilities, but even just the three options might help me be of more use to you —

MK

• July 13, 2017 at 1:13 pm #3158
Gavriel
Participant

Sure. Here was my process:

I took the two conditions K_L and O_ _ _ L to come up with these 4 scenarios.

1) O_K_L, 2) K_L_ _ _ O, 3) O_ _ _ L_K, 4) L_K_O

I eliminated the third scenario by using the condition that K or J must occupy the first slot.

For the K_L_ _ _O, scenario, this is a 7 slot scenario, and is the only scenario that involves K being the first element listed; therefore, it is the only way that K can fill the first slot.

In this scenario, the order must be K _ L M _ _ O.

Ergo, scenarios 1 & 4 must involve J as the first element.

This yields the following 2 options:

1) J _ O M K _ L 2) J_ L M K _ O

Thus, my three complete setups are:

1) K _ L M _ _ O
2) J _ O M K _ L
3) J _ L M K _ O

The question asks us to consider scenarios in which K is not first, leaving us with:

J _ O M K _ L & J _ L M K _ O

H and P are listed as free agents in the problem, and can therefore freely occupy slots 2 & 5 in these 2 scenarios. Subsequently, I am at a dead end and cannot see how slot 6 is a possibility for H.

• July 13, 2017 at 1:34 pm #3159
Mike Kim
Keymaster

Thanks so much, Gavriel — from what I can see from your work, you pretty much ended up at the same place I did in the book solution — forgive me if I’m missing something (it’s certainly been known to happen), but for the two scenarios you ended up with, it seems you have open slots 2 and 6 (that is, I’m not sure how you are seeing the second open spot as the fifth position) — MK

• July 13, 2017 at 1:44 pm #3160
Gavriel
Participant

Thanks for the quick reply! I was just thinking of it as a 6 slot problem when looking at that question, thus thinking that the penultimate slot was the fifth slot. Therefore, your solution makes sense, pretty much matches my work as well.

Really enjoying the book so far,
Gav

• July 13, 2017 at 5:11 pm #3161
Mike Kim
Keymaster

Ah — thought something like that might be the case — glad we could clear that up and great to hear that you are enjoying the book — MK

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