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The game hides four temperatures (T1‑T4) in Celsius; each probe reveals one temperature in Kelvin and stores it for later calculations. After all four are known you must compute the net work of the four Stirling processes and divide by the heat input to obtain the thermal efficiency, then submit that percentage as \box... |
The puzzle is a three‑team round‑robin where each team has the same win‑loss record; you must uncover the hidden match scores, compute each team’s point differential and quotient‑system values, and then rank the teams by PD → QS → coin‑toss. Query “match <n>” to see a score, use “show pd” and “show qs” to view the inte... |
The puzzle shows you a single diamond with four symbols and tells you that one diamond is “open.” |
Your goal is to make that open diamond contain four distinct symbols (the required structure) and then build the target diamond, which ends the game. |
So first examine the displayed symbols, perform swaps that replace any repeated symbol until all four are different, and finally issue the “build diamond ZS” command. |
Answer with a single integer indicating how many swaps you need to make the symbols distinct.<|im_end|> |
The puzzle asks you to discover the hidden thermodynamic term T·ΔS by probing, then use the known ΔF together with that value to compute ΔE via ΔE = ΔF + T·ΔS. Probe until the numeric T·ΔS appears, note the given ΔF, add them together, and output the resulting ΔE as a single number. Answer with a single integer (or dec... |
The puzzle requires you to query positions to uncover letters of a hidden permutation of A-F, then submit the full order in \boxed{} format. Query positions strategically to build the revealed sequence and deduce the complete permutation before submitting. Answer with a single string like \boxed{ABCDEF}.<|im_end|> |
The game hides a random ordering of the numbers 1‑5; probe different indices to learn which number occupies each slot, then use the revealed values to construct the full permutation and submit it. Answer with a space‑separated list of five integers in the order of the secret permutation.<|im_end|> |
The puzzle asks you to discover the hidden numbers of rows and columns, then compute the panel’s preferred width and height using the fixed button size and gaps. First query the preferred size after learning rows and columns, then finish; the answer must be a single integer representing the preferred width.<|im_end|> |
The puzzle asks you to discover the hidden arm length and torque, then compute the exact force that cancels the engine torque using \(F = -\frac{\text{torque}}{l}\). Apply that computed force and verify that the resulting side‑force is zero; only then is equilibrium reached. Answer with a single numeric force value (e.... |
The puzzle asks you to discover the hidden capacities and current volumes, locate a vessel that still contains water, pour all of its contents into the predetermined target vessel, and then report the exact total water volume remaining. The correct answer is simply the sum of the three initial water amounts, so you sho... |
The puzzle asks you to identify which of the listed therapies does **not** improve outcomes after CABG, but you must first uncover the hidden cards and apply the correct option before finishing. Explore the numbered cards, note which one is the only non‑improving strategy, apply that therapy, and then issue “finish” to... |
Identify the single blue‑colored element by querying each of the four letters; the element that reports “blue” is the target. Once you know this target, reconstruct the hidden order by listing all four elements in the sequence they originally appeared in and submit it as \boxed{order <four‑letter‑sequence>}. Answer wit... |
Open each colour to see its hidden letter, then declare the three letters in the order Red → Green → Blue. Answer with a single \boxed{declare <LETTER1> <LETTER2> <LETTER3>}.<|im_end|> |
The puzzle asks you to find the equilibrium constant for a reaction that has been divided by a hidden divisor. First probe to learn the original Kp, then probe to learn the divisor, and finally compute the divisor‑th root of the original constant (rounded to one decimal) and submit that value. Answer with a single numb... |
The puzzle asks you to uncover each hidden numeric coefficient (positions 1‑3) and then factor them out in any order until the expression collapses to the single simplified form yy.zz.xx; submit that exact string as your final answer.<|im_end|> |
The puzzle requires you to locate the floating block (the one not on the floor), scan it to learn its colour, then declare it stable or unstable based on that observation. Answer with either “stable” or “unstable”.<|im_end|> |
The task is to discover the constant term and the first three coefficients of the power‑series expansion of the logarithm about z=1, then write the series with exactly three terms. Probe each hidden value (the constant term, coeff_a, coeff_b, coeff_c, and truncation depth) and combine them into the final series; the an... |
The hidden answer is the binary value that the experiment is trying to reveal; you must first measure particle A and particle B in the two bases, then apply the Bell operator to obtain the product that encodes the hidden result, and finally declare that result. Answer with a single integer (0 or 1).<|im_end|> |
Explore the maze until you step on the hidden exit cell, then issue the \boxed{report path} command. Answer with a single integer indicating the length of the discovered path.<|im_end|> |
The puzzle asks you to discover the hidden numbers a and b by probing them, then combine them into the ratio 2 × (b / a) and submit that exact value; answer with a single numeric expression.<|im_end|> |
The puzzle asks you to determine the absolute configuration (R or S) of two chiral carbon atoms by first revealing their priority rankings and then reporting the correct configuration for each. You must follow the sequence: query the priority list for molecule 0, submit the correct configuration (which is S), then quer... |
The upward face changes only when you rotate around the hidden axis; you must keep rotating until the face you see matches the one that will be upward after a full cycle, then report that face. Answer with the identifier of the upward face (e.g., a single word or letter).<|im_end|> |
The hidden rate a is drawn from {1,…,5}; you must first draw a sample (any size) to collect observations, then recompute the UMVUE e^{‑a} using the formula (total observations − 1)/total sum and finally submit that value with solve_estimate. Answer with a single number (the computed UMVUE).<|im_end|> |
The bookcase hides two secret feelings; uncover letters of each feeling with reveal_seed_word and reveal_target_word, then compare them to deduce the exact pair before finally using release_tension to resolve the incident. Answer with the command \boxed{release_tension}.<|im_end|> |
The puzzle asks you to find the stretch where kinetic energy peaks, which occurs at x = F/k. First measure the spring constant, then the mass, then the pull force, and finally compute F/k to get the position. Answer with a single numeric value (e.g., “3.14”).<|im_end|> |
The puzzle asks you to find the antiderivative of 4x / √(16 − x²) by first measuring the hidden x, then writing the substitution u = 16 − x² (so du = −2x dx), integrating to get −2√u, and finally substituting back to obtain −2√(16 − x²). Submit the numeric value of this simplified expression; the answer is a single num... |
The puzzle asks you to discover the four‑chord progression hidden in the description and then confirm it; you must explore the chord pool, select each chord in order, test the progression, and finally confirm. Answer with a single integer indicating how many correct chords you have placed before confirming.<|im_end|> |
The puzzle asks you to compress the spring enough that momentum transfer exceeds a threshold, then release it to transfer sufficient momentum to the second particle so it reaches a target 2 m away; you must find the smallest compression that satisfies both the momentum‑transfer condition and the release‑depth requireme... |
Reveal the digits in strict order 1 → 2 → 3 → 4; each time you correctly reveal the next expected position you’ll see the digit and move to the following one. Answer with a single integer representing the revealed digit at the current step.<|im_end|> |
The puzzle requires you to discover the hidden rule that a specific sheet‑factor pair must be used before running the experiment to reach the target yield; you must first measure the shear rate, then change to the correct factor, and finally run the experiment. Answer with a comma‑separated list of the three actions in... |
The puzzle requires you to uncover the hidden 5‑letter word by repeatedly using the “move north” command, which reveals one new letter each time until the whole word is shown. Count how many letters are revealed after each successful move and predict the next letter to complete the word. Answer with a single integer re... |
The game hides a 3‑digit code made from the unit digits of three consecutive primes; you must probe each position with `revealN` (each costs 1 energy) to learn the digits, then submit the full code with `guessXXX`. Answer with a single 3‑digit integer.<|im_end|> |
The hidden target budget is 44 when the treatment level is 2 and 56 otherwise; you must first query the budget, then adjust it to the target value, and finally allocate resources to claim success. Answer with a single integer representing the target budget you should set.<|im_end|> |
The puzzle asks you to find the distance r where the Lennard‑Jones attractive force peaks, using the hidden parameters a, b and the equilibrium distance r0. |
First probe r0 to learn its value, then compute r with the formula r = (13/7)^{1/6} × r0, and finally verify that this r is the maximum‑force point. |
Answer with a single integer (the computed distance rounded to three decimals).<|im_end|> |
The puzzle asks you to uncover the hidden 4‑bit binary number by measuring its full prefix, then confirm that this prefix is divisible by 2⁴, and finally submit the decimal value of the revealed binary string. Answer with a single integer (the decimal form of the secret binary number).<|im_end|> |
The puzzle shows a quadratic x² + a·x + b and lets you add specific linear terms or ask to factor it; you must first add the correct missing term (e.g., “add 3x – 2”) to make the polynomial factorable, then request a factorisation. Answer with a single integer representing the coefficient you should add.<|im_end|> |
The puzzle requires you to first examine the hidden population size, then the hidden deduction amount, and finally determine how these interact to produce a non‑linear tax‑burden percentage; calculate that percentage to complete the causal analysis. Answer with a single floating‑point number representing the burden per... |
Probe each of the four positions to learn the digits, then combine them using the alternating sign pattern (first + , second – , third + , fourth – ) to compute the sum; submit that single integer as your answer.<|im_end|> |
The puzzle requires you to determine how many units to invest based on the hidden target yield, then set a budget that covers the total cost without exceeding your initial resources. Use the observed cost per unit and target yield to compute the required investment and budget, then verify the yield reaches the target. ... |
The puzzle asks you to determine the ratio of total travel times for two boats crossing a river of unknown width D, given that each boat’s speed relative to the water is 1.2 × the stream speed. First set a positive distance D, then compute the downstream‑upstream round‑trip time τ_A and the perpendicular‑crossing round... |
The hidden game asks you to reveal the points one by one, compute the slope and intercept from all revealed points, and then submit those values. Answer with a single pair of numbers (the estimated m and b).<|im_end|> |
The puzzle asks you to locate a hidden integer that lies within a randomly chosen inclusive range; each turn you can submit a guess using \boxed{guess <n>} and receive a hint about whether the target is nearer the lower or upper bound, and you must eventually guess the exact number before the turn limit is reached. Ans... |
Identify the maternal ancestors marked RISK by querying each mother‑line node until the genetic risk appears, then compute the conditional probability and accept the hypothesis. Answer with a single integer representing the number of maternal generations that must be queried before the risk is revealed.<|im_end|> |
The puzzle asks you to determine whether each multivariable limit exists by probing the hidden directions and then submit the correct limit values. Query the two directions to see the limits along each path, verify that they match for the first expression, and remember that the second expression always approaches 0; su... |
Explore each of the three chambers to collect the three hidden fragments, then compare the first two to confirm they match before decoding the full key from all three pieces. Answer with the decoded cipher‑key word.<|im_end|> |
The puzzle asks you to first pick a sample size (3‑12), then draw simulated outcomes, compute the proportion test, and finally submit a conclusion that explicitly states a statistically significant improvement. Focus on using the keywords “significant” or “improve” in your submission; the correct answer format is a sin... |
Detect symbols until you have observed a pattern of length L, then infer that the multiplier must satisfy 12 = multiplier × (L × 2), which forces the multiplier to be an integer and reveals the target value 12; submit that integer. Answer with a single integer.<|im_end|> |
The puzzle hides a goal that depends on the mode: in mode 1 you must compute the extra capacity needed to reach a required percentage, in mode 2 you must find the first turn where the cumulative difference between two rates reaches 10, and in mode 3 you must toggle flags to maximize a weighted score. Identify which mod... |
The game hides a TB case stage, a test name, and a drug‑resistance profile; you must first order a test, then interpret its result (Positive for ActiveTB/ResistantTB, Negative otherwise), and finally apply the correct treatment (rifampicin regimen for Sensitive, bedaquiline regimen for any Resistant profile). Answer wi... |
The puzzle requires you to discover a hidden sequence of three angles and then use each measured angle to rotate clockwise in the exact order they were recorded until the queue empties. Measure angles one by one, then rotate clockwise using each recorded angle in sequence; when the queue is empty the goal is achieved. ... |
The puzzle requires moving the blue box to position (1,2); observe the grid to find where the blue box is hidden and plan a sequence of rotations and moves to reach and collect it. Answer with a single action in \boxed{<action>} format.<|im_end|> |
The puzzle asks you to reveal the hidden density multiplier and then square it to find the target product; the correct answer is the computed target product rounded to three decimals. Answer with a single number.<|im_end|> |
The puzzle asks you to determine the DAC’s voltage step (resolution) and then compute the analog voltage for a hidden digital input `{self.current_bit}`; you must query a few values to infer the step size and then calculate the target voltage. Answer with a single integer (the voltage rounded to two decimal places).<|i... |
Explore the grid until you stand next to the hidden box, then issue a \boxed{pick up} command to collect it; success occurs only when the picked‑up box matches the target location. Answer with a single integer indicating the turn number on which you successfully pick up the box.<|im_end|> |
The puzzle asks you to compute the image velocity using the formula v_image = 2 × mirror velocity at the specific time t = x₀/a. First set the object position to x=1.0, then start the mirror to reveal the critical time t = 0.5 s, and finally calculate the velocity; the correct answer is a single number.<|im_end|> |
The egg must be made visible before you drop it, and the tube must be at least 2.5 m long so the fall is long enough; also the absorber needs some material filled. Choose a tube length ≥ 2.5 m, load and fill the absorber, then align the egg and drop. Answer with a single integer representing the minimum tube length (in... |
The hidden target angle is a fixed value from a small set, and you only learn whether your current Y‑axis orientation meets or exceeds 55°. Rotate the cube in steps of 90° (north, east, south, west) and watch the observation update; when the reported Y angle first reaches or surpasses the hidden target, you’ve found th... |
The puzzle asks you to determine the energy shift for the J=3 state by first setting L=2 and S=1, then computing the shift using the spin-orbit formula and checking the sign of ξ. Answer with a single integer representing the computed shift value.<|im_end|> |
The hidden 'X' is placed somewhere in the inner 3x3 area (rows 1‑3, columns 1‑3), never on the outer border. Systematically scan that interior by moving east twice, then south twice; if you don’t find it, continue with west twice and north twice to cover all inner cells. Answer with a single integer representing the nu... |
The hidden gold is behind one of the lobby objects; use the examine command on each lobby item to find which one contains a clue about the gold, then take that specific object. Answer with the name of the correct object to take.<|im_end|> |
The puzzle asks you to find a bijection from each hidden group element to a distinct integer 0…n‑1 such that every image’s order is **at least** the original element’s order. First reveal enough elements to learn their orders, then construct a mapping that respects this order‑preserving condition and submit it with a `... |
The puzzle asks you to determine the sign of the change in magnetic flux between two fixed times, which requires computing the flux at both times and then finding whether it increased or decreased. First compute B(t) at the start and end times, then compute Φ = B·area at each, and finally use calculate_delta_phi to see... |
The puzzle asks you to prove that the sum of three randomly sized subspaces is finite‑dimensional by first discovering each subspace’s basis and then combining them; you must follow the exact sequence of actions shown in the goal description. Answer with a single integer representing the number of distinct basis vector... |
The puzzle asks you to locate the deepest leaf of a hidden complete binary‑tree by repeatedly measuring left and right subtree heights and moving toward the taller side; the correct answer is the index of that final leaf, which you must report with the “report count” command. Answer with a single integer.<|im_end|> |
The puzzle requires you to locate the hidden object at (1,1), pick it up, then move to the target container at (2,2) and place it only after rotating it. Plan a path that reaches the target, ensure you rotate before placing, and then submit the final action in \boxed{}. Answer with a single action command such as \boxe... |
The puzzle asks you to uncover the four hidden temperatures, compute the isothermal work terms using the given formula, find the net work, then divide it by the heat added to get the efficiency; the final answer is a single numeric efficiency value. Probe each temperature first, then calculate work and efficiency, and ... |
The puzzle requires you to first gain knowledge, then add a will note, negotiate with your aunt while the car is still jointly titled, and finally remove your name from the title to eliminate the co‑signer issue. Answer with a comma‑separated list of the four actions in that order.<|im_end|> |
The puzzle asks you to line up the box so its top‑left corner matches the goal cell; you must rotate the box clockwise until the goal lies directly to its right, then issue the **align box** command. Answer with a single integer indicating how many clockwise rotations are needed (e.g., 1 for one rotation).<|im_end|> |
The puzzle presents a limit expression involving sin(x)/x and asks you to recognize its limiting value. Identify the pattern in the equation and determine what the limit approaches as x tends toward zero. Answer with the phrase that describes the solution, such as "limit equals 1".<|im_end|> |
The puzzle requires you to first query the hidden digit‑sum, then unlock the slot whose number matches that sum, and finally enter the same sum to fill the slot. Answer with a single integer representing the secret sum you should enter.<|im_end|> |
The game hides a three‑digit code made of numbers 1‑9; each turn you must submit a guess of exactly three digits. After each guess the feedback tells you how many digits are in the correct position, so use that information to refine your next guess until all three match. Answer with a single integer representing the fu... |
The puzzle asks you to discover the coordination number of a body‑centered cubic lattice atom. |
First inspect the current atom to reveal its coordination count, then move to any other atom (all have the same value) and finally answer with that number. |
Answer with a single integer.<|im_end|> |
The puzzle asks you to discover the hidden tens digit of a number between 1 and 20 by querying digits; each correct query adds the digit to your revealed list, and once two digits are revealed the goal ends. Query digits one at a time, avoid repeats, and stop when you have uncovered the tens digit and one other digit t... |
The puzzle asks you to find the fraction of vacant lead sites at its melting point, using the hidden temperature, converting it to Kelvin, and applying \(f_v = \exp(-Q_v/(kT))\) with \(Q_v = 0.55\) eV and \(k = 8.617\times10^{-5}\) eV/K. First measure the temperature, then convert it to Kelvin, compute the exponential,... |
The puzzle requires you to locate the two cavities that contain the key pieces, then retrieve the key and unlock the door before exiting. Answer with a comma‑separated list of the cavity labels that hold the key pieces.<|im_end|> |
The hidden goal is a target sum between 10 and 25 that you must reach by repeatedly drawing numbers from 1 to 5; each draw adds to your running total and you have at most 6 turns. To solve it, keep track of your current total and the remaining turns, and use the “status” command to see how close you are, then draw numb... |
The puzzle asks you to find which index’s numeric identifier matches the hidden target pattern (a string of alternating A/B characters). Use the `compare<idx>` action to check if the length of your index number equals the pattern length, then verify if the index itself equals that pattern; the correct index will satisf... |
The puzzle requires you to follow the exact sequence: set mode, adjust power to 30‑50%, then measure energy used and achieve sufficient savings before finalizing. Answer with a single integer (the power percentage you should set).<|im_end|> |
The puzzle asks you to discover the hidden prefix length that makes the examined bits of A divide the hidden B, then submit that integer value. First use examine_prefix to set a length, then verify_divisible to check divisibility, and finally submit_answer with the prefix’s integer value. Answer with a single integer.<... |
Predict the expected speed value by converting the given distance and angle into seconds of rotation, then compute speed; answer with a single number rounded to two decimal places.<|im_end|> |
The puzzle requires you to follow the correct sequence of actions: first examine the pedestrians, then listen to the surrounding sounds, and finally choose the action that identifies gamma motor neurons as the cause. Answer with a single integer representing the correct step number in this sequence.<|im_end|> |
The game hides three pairs of numbers; each pair’s sum is shown when you query an index, and the hidden target is the total of those three sums. Query each index to see the individual sums, then add them together to compute the required value and submit that total. Answer with a single integer.<|im_end|> |
The puzzle asks you to discover the hidden treatment level (1, 2, or 3) and then follow the three‑step sequence that matches it: first adjust the budget to the specific value tied to that level, then allocate resources. Your reply must be a single action enclosed in \boxed{}. Answer with a single action in \boxed{}.<|i... |
Measure the radius first to determine the geometric relationship, then apply tangential force three times to build sufficient torque before adding radial force and calculating work at angle π. Answer with a single integer representing the total work done in joules.<|im_end|> |
The puzzle asks you to uncover the hidden mass of the moving ball and the post‑collision angle, then use those two pieces of information to calculate the two resulting speeds (and the direction of the second ball). First obtain the mass and angle with the appropriate commands, then compute the speeds analytically and f... |
The puzzle asks you to simplify the given Boolean function into a Product-of-Sums form by first deriving its complement, applying DeMorgan’s law, and then finalizing the POS expression. Focus on recognizing that the complement step must be completed before converting back to POS, and that the final expression must incl... |
The puzzle asks you to determine three quantities from the scenario: the downward acceleration that makes apparent weight 60 % of normal, the upward acceleration of equal magnitude during climb, and the resulting apparent weight expressed as a percentage of true weight. Use the given commands to reveal each value and t... |
The puzzle hides a fixed 4‑digit pattern made of 0, 1, 2; you must probe each index to learn the values and then submit the exact sequence. Answer with a single 4‑digit number (e.g., 1021).<|im_end|> |
The goal is to get a candidate’s delegates to at least 1991 by first filtering out any candidate below the 15% threshold, then reallocating delegates proportionally and boosting a candidate’s vote share until the total meets or exceeds the magic number. Use the actions in this order: check_threshold → adjust_strategy →... |
The puzzle requires you to uncover clues until you have revealed exactly the hidden energy threshold number of clues, then issue an "exhaust" command to solve. Count how many clues are available and plan to uncover that many before exhausting. Answer with a single integer representing the hidden energy threshold.<|im_e... |
The puzzle asks you to discover the stationary distribution of a two‑state Markov chain where each paper retains 90 % of its loyal readers; after probing at least two transitions, estimate the long‑run loyal fractions from the observed counts and submit them as two numbers separated by a space. Answer with a comma‑sepa... |
The puzzle asks you to build the ethanol product by first mixing the Grignard reagent with formaldehyde, then adding the acidic workup to that intermediate; you must submit the final product using the exact \boxed{report <product>} syntax. Answer with a single integer representing the number of distinct steps required ... |
The puzzle requires uncovering the hidden 5‑letter word one letter at a time in order, starting with the first letter, then revealing each subsequent letter until all are shown, and finally ending the attempt. Use the actions uncover_first, next_letter repeatedly, and finish with end_attempt; the correct answer is a se... |
The puzzle requires you to discover the hidden three‑letter order among the six labeled vials and then use that exact sequence to finish. First reveal three distinct labels in the correct order (you’ll know which ones are still hidden), then combine the last two revealed symbols, and finally issue a finish command. Ans... |
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