Which one of the following could be an acceptable selection of the photographs to appear?

AndreaK on March 18, 2020

Hi @Kassidee,

This is a tough game! There really isn’t one best way to go about it. However, I will show you two ways here that you can give a try.

The first is a basic setup. Let’s start with setting up our board so it matches what we’re given in the stimulus. Three newspaper sections (L, M, S) and two photographs per section. Three photographers (F, G, H) will be distributed among the slots in the sections.

L _ _
M _ _
S _ _

F/G/H

Now, let’s take a look at what the rules offer us. There are a few to keep track of here.

1. For each photographer, at least one but not more than three of that photographer’s photos must appear.

With this rule, we get some hints about distribution. We have three photographers, and six slots to fill. We know everyone has to go at least once and no one can go more than three times. So, that leaves us with only two possible distributions. 3-2-1 or 2-2-2.

2. At least one photograph in the lifestyle section must be by a photographer who has at least one one photograph in the metro section.

If I were writing on a piece of paper, normally I would draw a box around the first slot of the L category and a second box around the first slot of the M category, to represent that they must hold the same game player in that box or in this case, the same photographer. This rule means L and M must have at least one player in common, and that’s what the boxes help show. Something to take note of is the “at least” language used in the rule. So, whatever player fills those two boxes could be on the game board a third time, when we think about how this rule works with the distributions from the rule before it. The player in these two boxes thus will go at least two times, and possibly a third.

3. The number of H’s photographs in the lifestyle section must be the same as the number of F’s photographs in the sports section.

Dissecting the implications of this rule, then, possible combinations include: 0 of each, 1 of each or two of each. This is one rule you could possibly make scenarios around, because it restricts the game somewhat. But, more on that later.

4. None of G’s photographs can be in the sports section.

With this rule, I think it’s best to just go ahead and stick it on our diagram like so:

L _ _
M _ _
S _ _ /G/
(Because this is digital and not paper, the double slashes replace what would otherwise just be a slash through G, indicating that it cannot go in sports.)

With this rule, we can also make a small deduction. If none of G’s photographs can go in S, then it must be true that one or more of G’s photographs fall somewhere between L, M, or both. It must also be true that least one of F or H (or both) must be in S.

Now, there really isn’t much for apparent deductions among the rules. You could stick with the above setup, keeping in mind the minor deductions we did make, and start tackling the questions. If there are many questions that provide additional premises in this game that restrict the game board more (otherwise called “if” questions because they start with “if”) then I would probably do those first and start getting a feel for the game. It may be a faster option to just work with the rules and the restrictions given in the question stems.

Alternatively, if you don’t feel comfortable with the uncertainty in this setup, you could make scenarios around the third rule, as mentioned above. Below I will show you how I would set that up.

Rule #3: The number of H’s photographs in the lifestyle section must be the same as the number of F’s photographs in the sports section.

If that’s the case, then there are three possible game boards we could make.

Game board #1: 0 of H in lifestyle, and 0 of F in sports.

L _ _ /H/
M _ _
S _ _ /G/ /F/

If we look at sports now, two of our three players can’t go in there. So, because those slots must still be filled, our remaining player, H, must fill both of them.

L _ _ /H/
M _ _
S: H H

Now let’s take a look at L. Because H can’t go in L (keeping in line with this scenario based on rule 3), that means only Fs or Gs (or both) can go in L. Combine that with rule two, and that also means F or G has to be in at least one slot of M.

L: F/G, F/G
M: F/G _
S: H H

Thus, that leaves us with a fairly restricted game board 1.


Game Board #2: 1 of H in lifestyle, and 1 of F in sports.

Still using rule #3 for our setups, we can plug in 1 of H in lifestyle, and 1 of F in sports.

L: H _
M: _ _
S: F _ /G/

Since G can’t go in S (rule 4, and it’s illustrated in our setup), and in this game board there is only one F in sports (keeping in line with rule 3 and the current scenario we’re making), the only remaining player that can go in S in this setup is H.

L: H _
M: _ _
S: F H

Since there is only one H in lifestyle for this setup (keeping in line with rule 3 and the current scenario we’re making), that means the remaining slot must go to either F or G.

L: H, F/G
M: _ _
S: F H

Now for metro, we have to think a bit deeper. In this setup, we have two Hs and one F placed for certain. Depending on distribution, that leaves a potential for one or two Gs in metro, or a third H in metro. However, be careful when it comes to F. We could put one F in metro, but not two. If we were to put TWO Fs in metro, we would have to put a G in lifestyle so that we have at least one G in our game board (rule 1). But if we put that G in lifestyle (with the H already there) then we don’t have at least one photographer in the lifestyle section matching at least one photographer in the metro section (metro having two Fs and lifestyle having an H and G), breaking rule 2.

Since we can’t put two Fs in metro, then, we thus know that at least one of those slots must go to H or G.

L: H, F/G
M: G/H, _
S: F H

That leaves us with a fairly restricted game board 2.

Game Board #3: 2 of H in lifestyle, and 2 of F in sports.

The final scenario based on rule #3 is 2 of H in lifestyle, and 2 of F in sports.

L: H H
M: _ _
S: F F

We know from rule 1 that we have to have at least one of each player in our game board. Since the slots in L and S are already filled, that means at least one G must go in M.

L: H H
M: G, _
S: F F

Rule 2 says that we need to have at least one player in common between L and M. Because L is already filled up with Hs, and we have one slot of M filled up with G, in order to satisfy rule 2 and have one player in common between L and M, that player must be H.

L: H H
M: G H
S: F F

That leaves us with a completely filled out game board 3!

However you prefer to approach this game, I hope this helps! Feel free to follow up if you have anymore questions. Unfortunately, this is not an easy game. So, don’t feel bad if you don’t see shortcuts right away—there aren’t many to be had here!

Irina on March 25, 2020

@kassidee,

This game requires us to match the authors of 6 photographs to the newspaper sections. There are a total of three sections - L M S - 2 photographs per section. Each of the photos is taken by one of three photographers - F G H.

__ __ __ F G H
__ __ __
L M S
~G
The following rules apply:

(1) For each photographer at least 1 but no more than 3 photographs must appear. This rule tells us that we must see each of the letters - F G H - at least once on the above diagram, but none of the letters could appear more than 3 times. This means that the number of photographs taken by each of the photographers must conform to one of the two patterns:

(a) 2-2-2 - each letter appears twice FF GG HH
(b) 3-2-1 -one letter appears three times, one two times, and one once.

These are the only combinations that result in each of the letters appearing at least once but no more than 3 times.

(2) At least one photograph in the L section must be by a photographer who has at least one photograph in the M section

This rule tells us that the same photographer must appear in both L and M section at least once.

L (1+) = M (1+)

(3) The number of H photographers in the L section must be the same as the number of F photographs in the S section.

Let's consider possible scenarios here. At most H could have two photographs in the L section:

H G F
H H F
L M S

This would require H to have one photograph in the M section per rule (2) and F to have two photographs in the S section. The remaining slot in the M section will be filled by G. This is a 3-2-1 scenario.

Alternatively, H could have 1 photograph in the L section:
H
H F
L M S

In this scenario, F must have one photograph in the S section, and the second slot in the S section must be filled by H since G cannot appear in S per the last rule. F/G/H are free variables for the rest of the slots as long as at least one of the variables appearing in L also appears in M: For example, this would be a valid combination:

G F H
H G F
L M S

Or H could have 0 photographs in the L section, and F could have 0 photographs in the S section:

In this case both of the slots in S would have to be filed by H:


F/G F/G/H H
F/G F/G/H H
L M S
~F
~G

H could also appear in one of the M slots, and the remaining slots must be filled by a combination of F & G.

~H(L) -> HH (S)

(4) None of the G photographs can be in the S section.
This rule tells us that G must have at least one photo either in L or M section.

The question asks us which of the following is an acceptable selection of photographs.

(A) is incorrect, we know that if none of the H photographs appear in L, H must appear twice in S.

(B) is correct and complies with all the rules per the scenario 3 above

(C) is incorrect because it violates rule (2), the same photographer must appear at least once in L and M.
(D) is incorrect because H must appear twice in S if it does not appear in L
(E) is incorrect because H appears four times in violation of rule 1.

Question 2 asks if both photographs in L are by H, which of the following must be true?

If we refer to our scenario above,

H G F
H H F
L M S

we see that (C) -exactly one by G must be true.

Question 3 asks if one photograph in L is by G and one by H, which of the following must be true?

If we refer to our diagram above, we can see that (D) -exactly 1 photograph by H is in S must be true.

H
H F
L M S

Question 4 asks which of the following could be true of photographs by F?

We can right away eliminate (C) and (E) because it violates rule (2) , the same photographer must appear at least once in the L and M section. We can also eliminate (B) because the number of F photographs in S cannot be higher than the number of H photographs in L, and this scenario only leaves one slot for H in L. Finally we can eliminate (D) because if F appears twice in the S section, H must appear twice in L, thus at least one of the photographers in M must be H per rule 2 leaving no space for G. Hence, we can conclude that (A) is the correct answer.

Question 5 asks if one of the photographs in L is by H and one by F , which of the following could be true?

We know that F must appear once in the S section per rule 3, and H must appear once in the S section as well since G cannot appear in S. H or F must appear in M, and the remaining slot in M must go to G.

H G H
F H/F F
L M S

(C) is the only option that could be true per the diagram above.

Question 6 asks if both photographs in one of the sections are by G, which of the following could be true?

We know that G cannot appear in S, so it could either appear in both sections of L and 1 section of M, or both sections of M and one section of M. In the first scenario, F must appear in M and H must take the remaining two slots in S since neither F nor G can appear in S in this case.

G F H
G G H
L M S

In a second scenario, H could either appear in G once and then F could appear in S once, or if no H appears in L, H must take both of the S slots leaving F as one of the photographs in L.

H/F G H
G G F/H
L M S

(E) is the only answer choice that could be true.

Question 7 asks if one of the photographs in the M section is by F and one is by H, which of the following could be true?

F/H F
G H
L M S

Since G cannot appear in S, we know that G must appear exactly one in L, and the second photographer in L must be either F or H per rule (2).

(C) is the only answer choice that could be true.

This is definitely a challenging and fairly long ago, but working on the initial setup and making all the key deductions is helpful in getting through the questions faster. Let me know if this makes sense and if you have any other questions.