Logic Challenge #24 - Groomer's Challenge

[perfectparadise1]

1. D
2. B
3. A
4. B
5. C
6. E

Rule 1: Lisa grooms more animals than any other groomer.
Rule 2: At least one poodle is groomed before any terrier is groomed.
Rule 3: Each groomer grooms at least two different types of animals.
Rule 4: Nancy grooms a poodle at 10 am.
Rule 5: No terrier can be groomed during the same hour that a poodle is groomed.
Rule 6: Mario does not groom a poodle first.

Since there are only 7 dogs and only one dog per slot, Lisa has to get 3 of them, one for 8am, 9am, and 10am. 7 breaks down into 3-2-2 and not other options of breaking 7 apart would allow for one of the groomers to have more animals than any other while only seeing one animal per time slot.

Furthermore, this means Lisa has to get at least one poodle as well as either another poodle and a terrier or a westie and a terrier or a poodle and westie.

Nancy already has a poodle for sure and can only have one other animal assigned to her since she is restricted to two animals by Rule 1. So Nancy will either get the westie or the terrier since each groomer HAS to see two different breeds.

Since Nancy has a poodle at 10am this means that the terrier cannot go at 10a.m. since a terrier and poodle cant be seen during the same time slot. Additionally, since there are 4 poodles and only a maximum of 3 of them can fill up one of the time slots (one for each groomer) and at least one poodle needs to be seen before a terrier then the terriers can only go during the 9am timeslot.

If Mario sees a dog during the 8am timeslot it HAS to be the westie. If he doesn't then he HAS to see a poodle at 10am.

Similarly Nancy has to see a poodle (rule 4) and either a terrier or westie.

1. Which one of the following must be true?

(A) Mario is assigned exactly one animal.
(B) Nancy is assigned exactly one animal.
(C) Lisa is assigned exactly two animals.
(D) Mario is assigned exactly two animals.
(E) Nancy is assigned exactly three animals.

In the deductions it was clear that Mario and Nancy HAVE to see 2 animals and Lisa sees 3.

2. Which one of the following must be false?

(A) Lisa grooms the westie.
(B) Nancy grooms two of the poodles.
(C) At least one of the terriers is groomed at 9 am.
(D) The westie is groomed before either of the terriers.
(E) Mario’s last appointment of the day is a poodle.

In the initial deductions it was made clear that Nancy has to see a one poodle and either the westie or terrrier. She can't have more than 2 animals but must see two different breeds. Seeing 2 poodles would violate these rules.

3. If the westie is groomed at 9 am, which one of the following must be true?

(A) Nancy does not have a grooming appointment at 8 am.
(B) Mario has a grooming appointment at 8 am.
(C) Both terriers are groomed at 10 am.
(D) Mario grooms the westie.
(E) Nancy does not groom a terrier.

Nancy can only have an 8am appointment if she has the westie so if the westie is to be seen at 9 then Nancy cannot have an 8am appointment. Since Nancy is already assigned to see a poodle at 10 and the 9 slot requires 2 terriers (as initially deduced) and now a westie, Nancy will have the only 2 appointments she can have filled.

4. The schedule of grooming appointments would be completely determined if which one of the following were true?

(A) Nancy grooms the westie
(B) Mario grooms the westie
(C) The westie is not groomed at 8 am.
(D) Mario’s first appointment is at 9 am.
(E) Lisa grooms the westie.

The Westie is a determining factor since it reveals who gets the terrier and other poodle by process of elimination. If Lisa does not get the Westie we know that she has to get a poodle at 8, a terrier at 9, and another poodle at 10 since she needs 3 dogs of 2 different breeds. We know that Mario cannot begin with a terrier and that a poodle needs to come before any terrier. Thus if Mario grooms the westie he has to do so at 8 and Lisa gets a poodle at 8. To satisfy the two breed requirement, Mario would have to get a poodle and allow Lisa and Nancy to get the poodles with Lisa getting 2 poodles. Since the terriers must go at 9 (as was deduced earlier) Lisa and Nancy must get the 2 terriers at 9. Lisa has a poodle at 9 and has to have 3 dogs and only poodles are left so another poodle takes her 10 spot. Nancy has a terrier at 9 and we are initially told that she sees a poodle at 10.


5. If Mario grooms a terrier, each of the following could be true EXCEPT:

(A) Nancy grooms the westie at 8 am.
(B) Lisa grooms the westie at 9 am.
(C) Mario grooms the westie at 8 am.
(D) Lisa grooms a terrier at 9 am.
(E) Nancy grooms a terrier at 9 am.

If Mario grooms a terrier he must do so at 9. IF he were to also see a westie at 8 there would be no way to allocate 2 breeds to each of the other 2 groomers since either Lisa would get a P and a T or leaving N with only a P or vice versa.

6. If the condition that Nancy grooms a poodle at 10 am is replaced with the condition that Nancy grooms the westie at 10 am, and if all other constraints remain in effect, each of the following must be true EXCEPT:

(A) Mario grooms a poodle.
(B) Nancy grooms a poodle.
(C) Lisa grooms a terrier.
(D) Mario grooms a terrier.
(E) Nancy grooms a terrier.

Forcing the westie to be seen at 10 by Nancy makes it so that Mario and Lisa have to each see one of a poodle and terrier to satisfy the 2 breed rule. There are only two terriers so one has to go to each of Lisa and Mario making it impossible for Nancy to have one.

[ryyang1118]

1. D
2. B
3. A
4. E
5. C
6. E

-Ryan

[ryyang1118]

3 Groomers: L, M, N
3 Types: P, T, W
3 Times: 8, 9, 10

The first and the third indented rules together determine the numerical distribution: L-M-N = 3-2-2.

The second indented rule: 1st P > T => T --> not 8
The forth and the fifth indented rule determines that T --> not 10.
Therefore T --> 9 and P --> not 9 (otherwise T cannot go anywhere)

Since every groomer needs to groom at least two different types of animals, each groomer has to take care one and exactly one dog other than a poodle. There are three scenarios based on the distribution of W.
Scenario 1: L grooms W: (don't forget the last indented rule that M cannot groom P at 8)
L: P....W...P
M: ......T....P
N: ......T....P
.....8....9....10

Scenario 2: M grooms W: dual option for W (8am or 9am)
L: P....T....P
M: W/../W..P
N: ......T....P
.....8....9....10

Scenario 3: N grooms W: dual option for W (8am or 9am)
L: P....T....P
M: ......T....P
N: W/../W...P
.....8....9....10

1) D
The deduced 3-2-2 numerical distribution requires that M is assigned exactly two animals

2) B
If Nancy grooms two poodles, then she cannot groom any other animal, and violate the rule that each groomer has to groom at least two types of animal
(A): Scenario 1
(C): Scenario 1, 2, and 3 can all support this case
(D): Scenario 2, 3 can support this case
(E): Scenario 1, 2, 3 can all support this case

3) A
If Westie is groomed at 9am, then we only have three possible solutions:
Scenario 1:
L: P....W....P
M: ......T....P
N: ......T....P
.....8....9....10

Scenario 2a:
L: P....T....P
M: .....W....P
N: ......T....P
.....8....9....10

Scenario 3a:
L: P....T....P
M: ......T....P
N: ......W...P
.....8....9....10

N does not have appt. at 8am in any of the above three scenarios
(B) Not true for scenario 1, 2a, and 3a
(C) T cannot be groomed at 8 nor 10 (see earlier analysis)
(D) Not true for scenario 1 and 3a
(E) Not true for scenario 1 and 2a

4) E
If L grooms W, then only scenario 1 is applied here. For scenario 1, all grooming schedules are completely determined (as opposed to scenario 2 and 3, where we have dual option for W)
(A) Scenario 3: W dual option
(B) Scenario 2: W dual option
(C) Three possibilities from Q3 (scenario 1, 2a and 3a)
(D) scenario1, 2a and 3 all allow for this condition

5) C
Scenario 1 and 3 apply here, and W cannot be groomed by M for both scenarios
(A) Scenario 3 allows N grooms W at 8
(B) Scenario 1
(D) Scenario 3
(E) Scenario 1

6) E
If Nancy grooms both T and W, then either L or M cannot groom two types of animals
In fact, only the following scenario exists for the local condition brought by Q6
Scenario Q6: dual option for P
L: P....P....T
M: ......P....T
N: P/../P....W
.....8....9....10
(A), (B), (C) and (D) are required for the template above.

[dena.haibi]

From the set up and constraints, you can figure out that Lisa grooms dogs in all three time slots, and that Mario and Nancy must groom exactly two dogs each, since there are seven animals to be groomed and Lisa must groom more animals than the other two. Since a poodle has to be groomed before any terriers are groomed, you know that no terriers can be groomed in the 8am slot. Since Nancy grooms a poodle in the 10am slot, and no terriers can be groomed at the same time as poodles, you know that the two terriers must be groomed at 9am. Since there are four poodles and each groomer must group two different breeds of dog, you know that Lisa must groom two poodles and either the westie or a terrier, and that both Mario and Nancy must each groom a poodle as well.

1. Which one of the following must be true?

(A) Mario is assigned exactly one animal.
(B) Nancy is assigned exactly one animal.
(C) Lisa is assigned exactly two animals.
(D) Mario is assigned exactly two animals.
(E) Nancy is assigned exactly three animals.

You know from the set up that Lisa must groom three animals, and Mario and Nancy must each groom exactly two animals. Thus, the answer is (D).

2. Which one of the following must be false?

(A) Lisa grooms the westie.
(B) Nancy grooms two of the poodles.
(C) At least one of the terriers is groomed at 9 am.
(D) The westie is groomed before either of the terriers.
(E) Mario’s last appointment of the day is a poodle.

Answer choice (A) could be true, so that is incorrect. Looking at (B), you know that Nancy grooms exactly two dogs and she must groom two different breeds, so that has to be false. (B) is the answer.

3. If the westie is groomed at 9 am, which one of the following must be true?

(A) Nancy does not have a grooming appointment at 8 am.
(B) Mario has a grooming appointment at 8 am.
(C) Both terriers are groomed at 10 am.
(D) Mario grooms the westie.
(E) Nancy does not groom a terrier.

If the westie is groomed at 9am, that means that all three groomers must groom dogs at 9am, since the westie and the two terriers must all be groomed at 9am. Also, since you know that Nancy has to groom a poodle at 10am, you know that Nancy cannot have a grooming appointment at 8am, since she only grooms two animals, one at 9am and the poodle at 10am. The answer is (A).

4. The schedule of grooming appointments would be completely determined if which one of the following were true?

(A) Nancy grooms the westie.
(B) Mario grooms the westie.
(C) The westie is not groomed at 8 am.
(D) Mario’s first appointment is at 9 am.
(E) Lisa grooms the westie.

The objective here is to force the westie into a given time slot. If the westie is groomed by either Nancy or Mario, the westie could be groomed in either the 8am time slot or 9am time slot. If you write it out, you can see that the westie would not be constrained to either spot in those scenarios, because Lisa's schedule would be poodle, terrier, poodle, while the other non-westie groomer's schedule would be 9am terrier, 10am poodle. In that way, the westie could be in the 8am or 9am spot with either Nancy or Mario. If Lisa grooms the westie, however, you know she would have to do so in the 9am slot, because she has to groom a poodle first and last. You then know that Mario and Nancy both have to groom terriers in the 9am slot. Also, you already know that Nancy must groom the poodle at 10am, and that Mario couldn't groom a poodle at 8am, so the only possibility left would be for him to groom a poodle at 10am, since both terriers and the westie are already accounted for. So if Lisa grooms the westie, the complete schedule is determined, and (E) is the answer.

5. If Mario grooms a terrier, each of the following could be true EXCEPT:

(A) Nancy grooms the westie at 8 am.
(B) Lisa grooms the westie at 9 am.
(C) Mario grooms the westie at 8 am.
(D) Lisa grooms a terrier at 9 am.
(E) Nancy grooms a terrier at 9 am.

As inferred before, Lisa must groom two poodles and Nancy and Mario must each groom one poodle. If Mario grooms a terrier, then the other animal that Mario grooms must be a poodle. You know that terriers can only be groomed in the 9am slot, and that Mario cannot groom a poodle in the 8am slot, so Mario's schedule must then be 9am terrier, 10am poodle. That means that Mario cannot groom the westie at 8am, so the answer is (C).

6. If the condition that Nancy grooms a poodle at 10 am is replaced with the condition that Nancy grooms the westie at 10 am, and if all other constraints remain in effect, each of the following must be true EXCEPT:

(A) Mario grooms a poodle.
(B) Nancy grooms a poodle.
(C) Lisa grooms a terrier.
(D) Mario grooms a terrier.
(E) Nancy grooms a terrier.

If Nancy grooms the westie at 10am, you know that she must groom a poodle at 8am, because she must groom one poodle, and poodles cannot be groomed at 9am. That means that both Mario and Lisa have to groom terriers at 9am, and that Mario grooms a poodle at 10am, and Lisa grooms poodles at 8am and 10am. That one condition determines the entire schedule. Comparing the schedule to the answer choices, you see that all of the choices must be true except for (E), because Nancy does not groom a terrier. The answer is (E).

[m055412]

1. D
2. A
3. A
4. C
5. B
6. E

Noah, when and how will the "Correct Answer Prize" be announced?

[cinderellamakeover]

1) D

2) A

3) C

4) D

5) E

6) E


- New Comer

[cinderellamakeover]

1) D

2) A

3) C

4) D

5) E

6) E


- New Comer

[noah]

1) D

2) A

3) C

4) D

5) E

6) E


- New Comer

Welcome, Newbie! And good luck.

BTW, in case anyone is interested, we use this to randomly choose the winner: http://www.random.org/ We can't find any hats.

[anthony.t.dinoto]

d
a
e
a
e
e

[tayjones]

1. D
2. B
3. A
4. E
5. C
6. E

[malingml]

SET UP:
-3 Groomers: Lisa, Mario, and Nancy (L.M.N)
-Schedule: 1-hour appointment slots available for each groomer at 8, 9 and 10
-7 animals with appointments: 4 poodles (p.p.p.p) 2 terriers (t.t), and 1 westie (w)
*Note: though it doesn't really matter in this game, when given 2 variables, (like
animals and groomers,) I usually prefer to make one set of variables upper case and
another lower case for easier distinction.
-No more than one animal is assigned to any time slot.

RESTRICTIONS/RULES:
1. Lisa grooms more animals than any other groomer
2. At least one poodle is groomed before any terrier is groomed.
3. Each groomer grooms at least two different types of animals.
4. Nancy grooms a poodle at 10 am.
5. No terrier can be groomed during the same hour that a poodle is groomed.
6. Mario does not groom a poodle first.

1. L grooms more animals than any other groomer

There are 3 time slots available for each groomer, so 9 slots available in total. Anytime I see a grouping game, I do the following: I put each item to be placed in each slot available and see how many slots are left. In other words, subtract the number of items to be placed by the slots available, in this case 9 minus 7. So we now know that there will be 2 slots left empty.

L _____ _____ _____
M _____ _____ _____
N _____ _____ _____

__8__ __9__ __10__


After drawing a quick sketch of the three times (8, 9, and 10) and the groomers along the Y-axis, I start to play with the numbers. If L grooms 1 animal, M and N cannot groom any, and 6 sad animals would be left dirty. So L MUST groom more than 1.

If L grooms 2, that leaves 5 animals. If 5 were left, either M or N would need to groom 3, which would contradict the rule that L grooms MORE than EITHER M or N. So, L must groom 3 animals, leaving 4 to be groomed. M and N must each groom 2, because, as stated earlier, each must groom fewer than L (fewer than 3). Now we can also see that L must groom an animal in each of the three time slots, (8, 9, AND 10) since no more than one animal can fill a time slot for an individual groomer.

L _____ _____ _____ ALL must be filled
M _____ _____ _____ 2 must be filled
N _____ _____ _____ 2 must be filled

__8__ __9__ __10__


2. At least one poodle is groomed before any terrier is groomed

Because there are only 3 times to choose from, (8, 9, or 10,) and a poodle must be groomed BEFORE any terrier, that no terrier may be groomed in an eight o clock time slot. So we should place a "t" under the 8 hour and cross it out. This leaves 6 slots available (3 nine slots and 3 ten slots) to place the 2 terriers.
L _____ _____ _____ ALL must be filled
M _____ _____ _____ 2 must be filled
N _____ _____ _____ 2 must be filled

__8__ __9__ __10__
_-t-_

3. Each groomer grooms at least two different types of animals

This rule, in conjunction with the first rule that allowed us to infer that Lisa would groom 3 animals, (note, it did NOT say 3 DIFFERENT animals,) and M and N would each groom 2, that at exactly 2 poodles will be groomed by L and that M and N will each groom exactly one poodle. L cannot groom 3 poodles, because then she would not satisfy this rule that each groomer will groom at least two different types of animal. That leaves 2 poodles left over, and neither M nor N may groom 2 poodles, because then they would not meet this criterion either.

4. Nancy grooms a poodle at 10 am

Now we can cross out one of our four poodles and place a "p" in Nancy’s 10 o’clock time slot.
ppp -p-
tt
w

L _____ _____ _____ ALL must be filled
M _____ _____ _____ 2 must be filled
N _____ _____ __p___ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__
5. No terrier can be groomed during the same hour that a poodle is groomed

__t, t__

L _____ _____ _____ ALL must be filled
M _____ _____ _____ 2 must be filled
N _____ _____ __p___ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__

Now we can see that both terriers must be groomed in the 9 o’clock hour because no terrier can be groomed in either the 8 or the 10 o’clock hours. Jot the 2 "t"s above the 9 o'clock slot, not indicating which spots they will fall into.

We can also infer from this rule that no poodle will be groomed in the 9 o’clock hour since if it were, no terrier would be allowed there.

6. Mario does not groom a poodle first.

__t, t__
L _____ _____ _____ ALL must be filled
M _X/w_ _____ _____ 2 must be filled
N _____ _____ __p___ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__

At the very least, we know that Mario may not groom a poodle in the 8 o’clock hour. This does not tell us, however, that he grooms ANY animal in the 8 o’clock hour. Because Mario grooms only 2 animals, his first animal could be groomed at either 8 or 9. So, because I can't appropriately format my diagram to indicate a crossed out "p" under M's 8 time slot, I'll place X/w in that space to represent it may be empty (X) or have a westie

Because M and N are only allowed to groom 1 poodle each, we are left with 2 more poodles that must be groomed by L. Because no poodle may be groomed in any 9 o'clock hour, L must groom a poodle in both the 8 and 10 o'clock hours. Because she must fill all of the 3 hours, she must groom either a westie or a terrier in the 9 o'vlock hour, as indicated below:

__t, t__
L __p___ __t/w_ __p__ ALL must be filled
M _X/w_ _____ _____ 2 must be filled
N _____ _____ __p__ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__
Before moving on to the questions, note that M MUST groom a poodle in either the 9 or 10 o'clock hour, whichever is his second (and last) appointment.

MOVING ON TO THE QUESTIONS...

1. Which one of the following must be true?

X(A) Mario is assigned exactly one animal.
X(B) Nancy is assigned exactly one animal.
X(C) Lisa is assigned exactly two animals.
(D) Mario is assigned exactly two animals.
X(E) Nancy is assigned exactly three animals.

We know that both Mario AND Nancy must EACH groom exactly 2 animals, and Lisa grooms exactly 3, so A, B, and C can immediately be eliminated.

At this point, we move on to D and see that it is correct. In a test, at this point we would bubble in answer choice D and move on. For the sake of clarity, though, we'll examine E as well. E must be false for the same reason A, B, and C were false.


2. Which one of the following must be false?

(A) Lisa grooms the westie.
(B) Nancy grooms two of the poodles.
(C) At least one of the terriers is groomed at 9 am.
(D) The westie is groomed before either of the terriers.
(E) Mario’s last appointment of the day is a poodle.

Because this is a "which must be false" question, if I don't see a clear answer popping out at first glance, I'll save it until after I've finished the questions starting with the word "If".

In this case, I start with A and am not initially sure whether or not it's correct, so I move on to B. As we inferred earlier, N only grooms 2 animals, and each groomer must groom at least 2 different animals. If N grooms 2 poodles, we will contradict these rules, so it MUST be false. Select B and move on!

3. If the westie is groomed at 9 am, which one of the following must be true?

On "If" questions, always start by making a quick sketch of the diagram with the conditions stated included. In this case, place a "w" above the 9 o'clock column

Because we know that both terriers must also be groomed in the 9 o'clock hour, we'll include them as well. Clearly, there are no remaining 9 o'clock slots available.

We can now see that each groomer MUST fill a 9 o'clock slot, L must fill EVERY slot, and N fills the 10 o'clock slot with a "p". Because N fills exactly 2 slots, we know that she cannot fill her 8 o'clock slot. Indicate this with an "X," or whatever symbol helps you the most.

After eliminating the "w" and two "t"s that go into the 9 o'clock hour, the only remaining animals are poodles. Because L must fill all of her time slots, she must groom a poodle in both the 8 and 10 o'clock hours.

That leaves an additional poodle to be groomed, and only M can groom it! He isn't allowed to groom a poodle as his first grooming appointment, so he must groom it in his 10 o'clock slot, leaving nothing in his 8 o'clock slot. Now we can move on to the answer choices.

(A) Nancy does not have a grooming appointment at 8 am.
Boom. Done. From the sketch we quickly drew, we can see that N may not have an appointment in her 8 o'clock slot. Since this is a "Must Be True" question, this is our answer!

(B) Mario has a grooming appointment at 8 am.
(C) Both terriers are groomed at 10 am.
(D) Mario grooms the westie.
(E) Nancy does not groom a terrier.

__t, t__

L __p__ __t/w_ __p__ ALL must be filled
M __X__ __t/w___ __p__ 2 must be filled
N __X__ __t/w___ __p__ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__


4. The schedule of grooming appointments would be completely determined if which one of the following were true?

As in question 2, which was a "must be false" question, if I don't see a clear answer popping out at first glance, I'll save it until after I've finished the questions starting with the word "If".


(A) Nancy grooms the westie.
Because N could groom the westie in either the 8 or 9 o'clock time slots, this is an incorrect answer.
(B) Mario grooms the westie.
Same explanation as A
(C) The westie is not groomed at 8 am.
As we can see from question 3, if the westie is groomed in the 9 o'clock hour, we still don't know which of the groomers will groom it. Incorrect answer choice.
(D) Mario’s first appointment is at 9 am.
As in C, we still don't know who grooms two of the terriers and who will groom the westie if this is the case.
(E) Lisa grooms the westie.
As this is the final answer choice remaining, it must be correct. Choose it and move on!

__t, t__

L __p___ __w_ __p__ ALL must be filled
M __X__ __t___ __p__ 2 must be filled
N __X___ __t___ __p__ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__



5. If Mario grooms a terrier, each of the following could be true EXCEPT:

__t, t__

L __p___ __t/w_ __p__ ALL must be filled
M __X__ __t___ __p___ 2 must be filled
N _?____ __?___ __p__ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__



(A) Nancy grooms the westie at 8 am.
Nancy could groom the westie at either 8 or 9 o'clock
(B) Lisa grooms the westie at 9 am.
Incorrect
(C) Mario grooms the westie at 8 am.
CORRECT! Since Mario must groom the terrier at 9 o'clock, he must groom a poodle at 10 since his first animal may not be a poodle. He grooms EXACTLY 2 animals, so he's unable to groom any animal at 8.
(D) Lisa grooms a terrier at 9 am.
(E) Nancy grooms a terrier at 9 am.

6. If the condition that Nancy grooms a poodle at 10 am is replaced with the condition that Nancy grooms the westie at 10 am, and if all other constraints remain in effect, each of the following must be true EXCEPT:

__t, t__

L __p___ __t___ __p__ ALL must be filled
M _X___ __t___ __p___ 2 must be filled
N __w___ __X___ __p__ 2 must be filled

__8__ __9__ __10__
_-t-_ __-t-__


Because M and N each groom 1 poodle exactly, with this new condition, N must groom a poodle at 8, (as no poodle may be groomed in the 9 slots where the two terriers are designated.)

Similarly, M must groom a poodle at 10.

Because M and L are the only groomers available to groom the two terriers in the 9 o'clock slots, they must!

(A) Mario grooms a poodle.
Incorrect, this MUST be true
(B) Nancy grooms a poodle.
Incorrect, this MUST be true
(C) Lisa grooms a terrier.
Incorrect, this MUST be true
(D) Mario grooms a terrier.
Incorrect, this MUST be true
(E) Nancy grooms a terrier.
CORRECT! Not only does this not NEED to be true, but it CANNOT be true!

DONE!!!

[jmichaelchin]

Ryan did this one the best, figuring out that there are three templates for frames, which make this one a breeze. Overall, I thought this was one of the easier Atlas ones, but I still didn't do as well as I wanted.

Setup:

Variables: PPPPTTWXX
This game was underfunded -the were too few dogs for hours so I put in two Xs that would be placed in unused time slots. This wasn't actually very useful the way I did it.

Use the hours as the base and NML as a the vertical element

Place P in Nancy's 10 o'clock slot - now write a not law saying terriers can't got at 10 (because of that P)

P<T so you know that a terrier can't be at 9'oclock - you know know the two Ts have to go at 9.

write out the PT not law vertically

Write that each person needs to do two different breeds.

---

Inferences:

Write off the bat, we get the numerical distribution. Lisa will do 3, the others will do two.

Dog variation. I didn't see this at first, and it's very helpful. Since there needs to be variation and there are so many Ps, each person needs a T or a W to provide a mix. Also means that whoever gets the W can't have the T and thus the other two get Ts, at 9 o'clock to boot. This led to Ryans idea for frames/templates, giving each person the W in each scenario.

But in case you didn't get that (I definitely didn't) let's see how it plays without it.

Questions

1. This comes directly from the numerical dist, which is an easy inference. D - Mario has to do two because we know Lisa does 3.

2. B. Again from our initial and easy inferences, N can't do two Ps because that would exhaust her dog limit and she wouldn't have the required variation.

3. Don't panic. Diagram this out with T/W down the middle line. when in doubt diagram. We see right off the bad that A is right, Nancy can't have an 8AM appt because she has exhausted her dog limit. C is absurd by the way - easy elim.

4. this one killed me at first. but in retrospect, you should look at the areas of greatest restriction, Lisa and W/T. It's also dead easy if you discovered Ryan's method early.

it's also easy to think it's mario, because you forget the W can also go at 8 no problem.

But go to Lisa and the westie and you see it' changes everything.

5. At this point you can get rolling. If mario does the westie, then he can't do a terrier. so C should stand out. this is back to the notion that the TTW have to be spread out. thank god for that rule

6. Again. Rolling. Make a new diagram with the W for nancy instead of the P. This makes things more restrictive. You can place the Ts for 9 for M and L. Place Ps for L. a P at 10 for M. Go through the rules and we see that only E not only not necessarily true, but impossible!!