Question

Which of the following day is the play day?

• A. Monday
• B. Tuesday
• C. Wednesday
• D. Thursday
• A. One
• B. Two
• C. Three
• D. Four
• A. Monday
• B. Tuesday
• C. Wednesday
• D. Thursday
• A. Monday
• B. Tuesday
• C. Wednesday
• D. Thursday
• A. Biology day is after Chemistry day
• B. Physics day is on Wednesday
• C. Play day is on Monday
• D. Chemistry day is earlier than Physics day

Answer 1

The Correct Option is B

Step 1: Chain around the Play day
From (iv) and (v): the three consecutive days must be Physics — Play — Social Science (Phy/Play/SS in order). This triple must fit inside Mon–Sat without touching Sunday.
Step 2: Test each option for the Play day
[-2mm]
Play = Monday: Then Phy would be Sunday (not allowed; Sunday is a holiday). Reject.
Play = Tuesday: Then Phy = Monday, SS = Wednesday. This fits the week. Keep as a candidate.
Play = Wednesday: Then Phy = Tuesday, SS = Thursday. From (vi), SS and Bio must be three days apart (two days in between), so Bio would have to be \underline{Sunday or Monday}. Sunday is a holiday; Monday Bio forces Chem on Sunday (since Bio is the day after Chem), impossible. Reject.
Play = Thursday: Then Phy = Wednesday, SS = Friday. From (vi), SS (Fri) three apart gives Bio = \underline{Tuesday or Monday}.
If Bio = Tuesday, then Chem = Monday. But (ii) demands Math earlier than Chem and not first/last; earlier than Monday is impossible. Reject.
If Bio = Monday, Chem = Sunday (holiday). Reject.
Play = Friday/Saturday: SS would be Saturday/Sunday respectively; Saturday case leaves no room for the two-day gap with SS and the Chem–Bio adjacency, and Sunday is a holiday. Reject. Step 3: Complete the schedule for the valid case (Play = Tuesday)
We have: Mon = Phy, Tue = Play, Wed = SS. From (vi), SS (Wed) and Bio must be three days apart, so Bio = Saturday. Then from (iii) Chem must be the day before Bio, i.e., Friday. By (ii), Math is earlier than Chem and neither first nor last, so Thursday suits Math. Final layout (Mon–Sat): Phy, Play, SS, Math, Chem, Bio — all conditions satisfied.
Conclusion: The only consistent placement is Play on Tuesday.

Answer 2

The question asks which day is the play day, out of Monday, Tuesday, Wednesday, and Thursday. Rather than guessing each day and checking it, we can build the entire week forward from the clues just once, and then simply compare that result against the four options.

Clues (vi) and (viii) tell us Physics, Play, and Social Science fall on three consecutive days in that fixed order. Since Sunday is a holiday, this block cannot touch day 1 or day 6 of the Monday-Saturday week without breaking the "day before" or "day after" links to Sunday. Working through the remaining constraints, Biology falling immediately after Chemistry (v), a two-day gap between Biology and Social Science (vii), and Mathematics falling before Chemistry while being neither the first nor the last day (iv), the only placement that lets Mathematics, Chemistry, and Biology fit into the leftover three days without contradiction is: Physics = Monday, Play = Tuesday, Social Science = Wednesday, Mathematics = Thursday, Chemistry = Friday, Biology = Saturday.

Now checking this schedule against each option:

1. Monday: Monday is occupied by Physics in the derived schedule, not Play.
2. Tuesday: Tuesday is exactly where Play falls in the derived schedule, matching this option.
3. Wednesday: Wednesday is occupied by Social Science, not Play.
4. Thursday: Thursday is occupied by Mathematics, not Play.

Only Tuesday matches the play day in the fully worked-out week.

Therefore, the correct answer is Tuesday.

Answer 3

Rather than testing every day of the week individually, we can use the shape of the leftover days. Clues (vi) and (viii) force Physics, Play, and Social Science into three consecutive days in that order, which leaves exactly three other days for Mathematics, Chemistry, and Biology. Since Chemistry and Biology must always sit side by side, those two need two consecutive days out of the three leftover days, leaving Mathematics as the remaining single day. Let's test each candidate play day using this leftover-shape check:

1. Monday: If Play were Monday, Physics would fall on Sunday, which is a full holiday and cannot hold a subject. This is impossible on its own.
2. Tuesday: If Play is Tuesday, Physics is Monday and Social Science is Wednesday, leaving Thursday, Friday, Saturday as one uninterrupted leftover block. Chemistry-Biology can sit on Friday-Saturday, leaving Mathematics on Thursday, which is neither the first nor last day, and does come before Chemistry, so every clue is satisfied.
3. Wednesday: If Play is Wednesday, Physics is Tuesday and Social Science is Thursday, leaving Monday, Friday, Saturday, which is not one continuous block, Monday is isolated from Friday-Saturday. Chemistry-Biology would have to sit on Friday-Saturday, forcing Mathematics onto Monday, the very first day of the week, which directly breaks the rule that Mathematics cannot be first.
4. Thursday: If Play is Thursday, Physics is Wednesday and Social Science is Friday, leaving Monday, Tuesday, Saturday, again not a single continuous block. Chemistry-Biology would need to sit on Monday-Tuesday, forcing Mathematics onto Saturday, the last day of the week, which directly breaks the rule that Mathematics cannot be last.

Only placing Play on Tuesday leaves the remaining three days as one clean, unbroken block that can hold Mathematics, Chemistry, and Biology without breaking any rule.

Therefore, the correct answer is Tuesday.

Answer 4

From Q181’s completed schedule: Mon = Physics, Tue = Play, Wed = Social Science, Thu = Mathematics, Fri = Chemistry, Sat = Biology. Step 1: Identify positions
Physics = Monday (Day 1), Biology = Saturday (Day 6). Step 2: Count the gap days in between
Between Monday and Saturday: Tue, Wed, Thu, Fri = 4 days gap. Step 3: Verify no wrap-around
We only count within the same week’s schedule (Mon–Sat), so no circular count is needed.

Answer 5

The question asks how many days form the gap between Physics day and Biology day. From the fully worked-out week (Physics = Monday, Play = Tuesday, Social Science = Wednesday, Mathematics = Thursday, Chemistry = Friday, Biology = Saturday), Physics falls on Monday and Biology falls on Saturday. The "gap" refers to the days that lie strictly between these two, not counting Monday or Saturday themselves. Let's check this against each option:

1. One: A gap of one day would mean only a single day separates Physics and Biology, placing them close together, such as Monday and Wednesday. That is not the case here.
2. Two: A gap of two would mean two days lie between them, such as Monday and Thursday. Physics and Biology are much further apart than that.
3. Three: A gap of three would place Biology on Friday if Physics is Monday. Biology is actually on Saturday, one day later than that.
4. Four: Counting the days strictly between Monday and Saturday gives Tuesday, Wednesday, Thursday, and Friday, exactly four days. This matches the actual positions of Physics and Biology in the schedule.

Since Physics is on Monday and Biology is on Saturday, exactly four days (Tuesday, Wednesday, Thursday, Friday) fall between them.

Therefore, the correct answer is Four.

Answer 6

Once the full week is worked out, Physics falls on Monday and Biology falls on Saturday. To count the "gap" between two days, we can use the simple rule that the gap equals the distance between their positions in the week, minus one, since the gap only counts the days strictly in between, not the two endpoints themselves. Numbering Monday as day 1 through Saturday as day 6, Physics is at position 1 and Biology is at position 6, giving a distance of \( 6 - 1 = 5 \), and therefore a gap of \( 5 - 1 = 4 \). Let's check what each option would imply about Biology's position, working backwards from the formula:

1. One: A gap of one implies a distance of two positions from Physics, which would place Biology on Wednesday (day 3), not Saturday, contradicting the actual schedule.
2. Two: A gap of two implies a distance of three positions, placing Biology on Thursday (day 4), which again does not match Biology's actual position on Saturday.
3. Three: A gap of three implies a distance of four positions, placing Biology on Friday (day 5), still one day short of where Biology actually falls.
4. Four: A gap of four implies a distance of five positions, placing Biology on Saturday (day 6), which matches Biology's true position in the schedule exactly.

Only a gap of four correctly reproduces Biology's actual position of Saturday when counted forward five positions from Physics on Monday.

Therefore, the correct answer is Four.

Answer 7

Rebuild the fixed blocks from the rules
From the instructions:
(i) One day is Play; the rest (Mon–Sat) are single-subject days; Sunday is a holiday.
(ii) Physics is on the immediate previous day of Play.
(iii) Social Science is on the immediate next day of Play.
Hence, the three consecutive days must be Physics — Play — Social Science.
Eliminate impossible placements for Play
Play cannot be Monday (would force Physics on Sunday, a holiday).
Play cannot be Wednesday if we also respect: Biology and Social Science have a two-day gap between them, and Biology is the day after Chemistry; this creates a contradiction with Sunday.
Play cannot be Thursday (gives contradictions with Mathematics being earlier than Chemistry and not first/last).
The only consistent position is Play = Tuesday. Therefore, Physics = Monday and Social Science = Wednesday.
Complete the week to cross-check
With SS on Wednesday, the two-day gap to Biology puts Biology = Saturday, so Chemistry = Friday (Bio is immediately after Chem). Mathematics is earlier than Chemistry and not first/last, so Mathematics = Thursday.
Final arrangement: Mon–Sat = Physics, Play, Social Science, Mathematics, Chemistry, Biology. All rules fit.
Thus, Social Science day is Wednesday.

Answer 8

The question asks which day is Social Science day. Building the week directly, clues (vi) and (viii) fix Physics, Play, and Social Science as three consecutive days in that order, and this block can only sit at Physics = Monday, Play = Tuesday, Social Science = Wednesday without breaking any of the other clues about Mathematics, Chemistry, and Biology, which then fall on Thursday, Friday, and Saturday respectively. Let's compare each option to this result:

1. Monday: Monday is taken by Physics in the resolved week, not Social Science.
2. Tuesday: Tuesday is taken by Play, not Social Science.
3. Wednesday: Wednesday is exactly where Social Science falls, immediately after the play day (Tuesday), matching clue (viii) directly.
4. Thursday: Thursday is taken by Mathematics, not Social Science.

Social Science sits immediately after the play day, and since Play is Tuesday, Social Science falls on Wednesday.

Therefore, the correct answer is Wednesday.

Answer 9

Rather than reading Social Science day directly off the play day, we can work it out from the other end of the week and cross-check. From clue (iv), Mathematics must come before Chemistry while not being the first or last reading day, and from clue (v), Biology always falls the day right after Chemistry. Once the Physics-Play-Social Science block is fixed at Monday-Tuesday-Wednesday, only Thursday, Friday, and Saturday remain for Mathematics, Chemistry, and Biology, and the only order that fits all their rules is Mathematics-Thursday, Chemistry-Friday, Biology-Saturday. Using clue (vii), the two-day gap between Biology and Social Science, we can now work backwards from Biology's confirmed position on Saturday to find Social Science: counting back three days from Saturday lands on Wednesday. Let's check each option against this backward count:

1. Monday: Counting three days forward from Monday reaches Thursday, not Saturday, so Monday does not satisfy the required gap to Biology.
2. Tuesday: Counting three days forward from Tuesday reaches Friday, not Saturday, so this does not fit either.
3. Wednesday: Counting three days forward from Wednesday reaches exactly Saturday, matching Biology's confirmed day precisely.
4. Thursday: Counting three days forward from Thursday overshoots past Saturday into the next week, so this cannot be correct within the six-day schedule.

Working backward from Biology's fixed position on Saturday using the two-day gap rule confirms that Social Science must fall on Wednesday.

Therefore, the correct answer is Wednesday.

Answer 10

Use the established sequence
From Q183’s reconstruction: Mon–Sat = Physics, Play, Social Science, \underline{Mathematics}, Chemistry, Biology.
Why must Mathematics be Thursday?
Rule: “Mathematics is neither on the first nor the last day but earlier than Chemistry.”
In the arrangement above, Chemistry is Friday; the only remaining day earlier than Friday that is not first/last and not already occupied by Physics/Play/SS is Thursday.
Therefore, Mathematics day is Thursday.

Answer 11

The question asks which day is Mathematics day. From the fully resolved week, Physics (Mon), Play (Tue), Social Science (Wed), Mathematics (Thu), Chemistry (Fri), Biology (Sat), let's check each option against clue (iv), which says Mathematics must be earlier than Chemistry and must be neither the first nor the last reading day:

1. Monday: Monday is the very first reading day of the week, and clue (iv) explicitly rules out Mathematics being on the first day. Also, Monday is already taken by Physics.
2. Tuesday: Tuesday is already assigned to Play, not a subject day, so Mathematics cannot fall here.
3. Wednesday: Wednesday is already assigned to Social Science, so this day is unavailable for Mathematics.
4. Thursday: Thursday is free in the schedule, sits before Chemistry (Friday), and is neither the first day (Monday) nor the last day (Saturday) of the week, satisfying clue (iv) completely.

The only day left over after fixing Physics, Play, Social Science, Chemistry, and Biology, which also respects "before Chemistry, not first, not last", is Thursday.

Therefore, the correct answer is Thursday.

Answer 12

With the Physics-Play-Social Science block fixed at Monday-Tuesday-Wednesday, only Thursday, Friday, and Saturday remain for Mathematics, Chemistry, and Biology. Since Biology must always sit the day right after Chemistry, these two need to occupy two consecutive days out of these three, leaving Mathematics as whichever single day is left over. There are only two ways to place a consecutive Chemistry-Biology pair inside Thursday, Friday, Saturday: either Chemistry-Biology takes Thursday-Friday, leaving Mathematics on Saturday, or Chemistry-Biology takes Friday-Saturday, leaving Mathematics on Thursday. Let's test each option against these two possibilities and the rule that Mathematics is neither first nor last:

1. Monday: Monday is already fixed as Physics day, and it is also the very first reading day, so Mathematics cannot be placed here for two separate reasons.
2. Tuesday: Tuesday is already fixed as the play day, leaving no room for Mathematics here.
3. Wednesday: Wednesday is already fixed as Social Science day, so Mathematics cannot be placed here either.
4. Thursday: This matches the second valid placement above, Chemistry-Biology on Friday-Saturday, leaving Mathematics on Thursday, which is neither the first day (Monday) nor the last day (Saturday) of the week.

The other possible placement, Mathematics on Saturday, is ruled out because Saturday is the last reading day of the week, which clue (iv) forbids for Mathematics. That leaves Thursday as the only workable day.

Therefore, the correct answer is Thursday.

Answer 13

Reference arrangement (validated in Q183):
Mon–Sat = Physics, Play, Social Science, Mathematics, Chemistry, Biology.
Check each option explicitly
(A) True: Biology (Saturday) is indeed after Chemistry (Friday).
(B) False: Physics is Monday, not Wednesday.
(C) False: Play is Tuesday, not Monday.
(D) False: Chemistry (Friday) is later than Physics (Monday), not earlier.
Therefore, only (A) is correct.

Answer 14

The question asks which of four statements about the schedule is correct. Using the fully resolved week, Physics (Mon), Play (Tue), Social Science (Wed), Mathematics (Thu), Chemistry (Fri), Biology (Sat), let's test each statement against it directly:

1. Biology day is after Chemistry day: Chemistry falls on Friday and Biology falls on Saturday, and Saturday does indeed come after Friday, so this statement holds true.
2. Physics day is on Wednesday: Physics actually falls on Monday in the resolved schedule, not Wednesday, so this statement is false.
3. Play day is on Monday: Play actually falls on Tuesday, not Monday, since Physics occupies Monday, so this statement is false.
4. Chemistry day is earlier than Physics day: Chemistry is on Friday while Physics is on Monday, so Chemistry actually comes later in the week than Physics, not earlier, making this statement false.

Only the first statement, that Biology day comes after Chemistry day, matches the resolved week.

Therefore, the correct answer is Biology day is after Chemistry day.

Answer 15

Rather than rebuilding and re-checking the whole week for every statement, it helps to first ask whether a statement can be confirmed or denied directly from a single original clue, before reaching for the full schedule. Let's go through each statement this way:

1. Biology day is after Chemistry day: Clue (v) directly states that Biology day is the immediate next day after Chemistry day. If Biology is the day right after Chemistry, it is automatically also simply "after" Chemistry in the broader sense, so this statement follows straight from clue (v) alone, with no need to place actual weekdays at all.
2. Physics day is on Wednesday: No single clue fixes Physics on a specific weekday directly, this requires building out the full block, Physics-Play-Social Science must start on Monday, as forced by the remaining clues, which places Physics on Monday, not Wednesday, so this statement is false.
3. Play day is on Monday: Again, this needs the full block placement; once Physics is fixed on Monday, Play necessarily falls the next day, Tuesday, not Monday, so this statement is false.
4. Chemistry day is earlier than Physics day: Using the completed week, Chemistry falls on Friday while Physics falls on Monday, meaning Chemistry actually comes later in the week, not earlier, so this statement is false.

Only the first statement, that Biology day is after Chemistry day, can be confirmed directly from a single original clue without needing to work out any specific weekday, and it is also consistent with the completed schedule.

Therefore, the correct answer is Biology day is after Chemistry day.