Turing Machine

01Discover the game

Turing Machine is a logical investigation. Instead of questioning other players, you present proposals to a machine made of perforated cards. It answers only yes or no. You have to understand what each auditor is looking at, then combine the information to find a single three-digit code.

The basic game of the Masqué Scorpion is played by 1 to 4 players, in approximately 20 minutes, with very different problems of difficulty. We explain the mode Classic, then the solo and cooperative adaptation. Extreme modes and Cauchemar change the available information and are not mixed with this initiation.

The overall difficulty is Hard success depends on the quality of the deductions and on the choice of questions that really eliminate possibilities. No complicated calculation is necessary, but a misinterpreted answer can make the whole survey go in the wrong direction.

02Equipment

The box includes 45 perforated cards, organized in three sets of fifteen cards: for each game, values 1 to 5 in the three colors and shapes. It also contains 48 maps Criteria, 95 verification cards, 4 aides-memoires used as screens, 50 note sheets, 1 felt, 1 Machine tile, 1 perforated card holder to be assembled and the booklet of problems and rules.

The code has a blue triangle digit, a yellow square digit and a purple circle digit, each between 1 and 5. The shapes complete the colors; always keep the same order to note your codes. A code such as 345 means here blue 3, yellow 4, purple 5.

A Criteria card presents several possible rules; the verifier only uses one for the chosen problem. The Verification card below performs this secret test. These are not cards which are freely read the reverse to know the answer.

03The goal

Find the code that satisfies all the auditors. In competition, you have to find it before the others, or with fewer questions if several people succeed in the same round. The winner is not necessarily the one who asks the most questions.

The machine does not tell you: "this number is exactly the right one." It says: "this proposal respects, or does not meet, my criterion." If an auditor examines only "blue is greater than 3", he will answer yes with blue 4 and with blue 5. The other two numbers are of no importance for this precise test.

04Preparing a problem

Place the Machine tile in the center and assemble the support. Store the perforated cards so as to find each value easily. The booklet recommends not to disassemble the support at the end of each part.

Choose an introduction problem in the booklet, or a Classic problem on the official site. Its sheet shows the letters of the auditors used, from A to D, E or F, and for each one a criteria card number and a verification card number. exactly the numbers and associations indicated. Don't create a problem by randomly mixing cards: it might have no solution or more.

Lays out each card Criteria clearly visible in front of its letter and its card Verification face hidden next door. A single card Verification has several color markers: check the required mark, not only the number that attracts the eye. The eraseable marking of the letter on the back, provided for in the booklet, avoids accidental exchanges.

Each receives an aide-mémoire and a sheet of notes. Note the problem number and bar the columns of the absent auditors. The solution remains hidden until the final check. The three sets of perforated cards do not limit the game to three players: if a card is missing temporarily, wait for someone to finish their test to borrow.

05A complete handle

Compose a proposal

Everyone thinks and plays individually, in the same handle. Choose three perforated cards, one for each color, and overlay them in the right direction. There is only one common hole left. Write the proposal on the line of the current handle.

This proposal does not change during the round. You don't have the right to test 345 with A, then replace the 3 with a 4 before questioning B. A new proposal awaits the next round.

Interview up to three auditors

Choose the auditors who can teach you something. up to three questions during this handle. You do not have to use all three. Slide the relevant check card under your perforated cards, respecting the orientation marks. Read only the answer in the common hole.

Note V or X in the right column, then hand over the Check Card face down to its location. The answers are personal: do not announce your results to others during a competitive game. Note all the questions, even those that seem useless after the fact, because their number separates the winners.

Deduct a criterion

Compares the proposal to the text of the Criteria map. A yes confirms that the proposal meets the secret criterion; a no eliminates the criteria that it would have met. This may be sufficient to identify the criterion, or only to reduce the possibilities.

An essential point: a false answer does not state that all the elements of your proposal are false. If A only looks at the blue colour, its no directly informs neither yellow nor purple. Similarly, a yes to a comparison may suit many different values.

Some maps examine parity, order, sum or repetition. Read exactly the words: pair is not synonymous with superior, "a pair" is not "at least two identical digits" if the card distinguishes the triple, and the verified criterion remains the same throughout the survey. The explanations of each family of cards in the booklet are used to remove these difficulties; do not replace their formulation with an approximate rule.

Announce the end together

When everyone has finished their questions and deductions, count to three. Each shows simultaneously the thumb up if he thinks he has the code, or down otherwise. If no one is ready, start a new handle with a new proposal.

If at least one person thinks that he or she has found it, he or she clearly and secretly writes his or her final code. It does not have to be the proposal tested during this round: deductions may have led to another combination.

Check without ruining the game

Those who have announced a code consult the solution of the problem in the booklet or the button provided on the official website. If many are right, the one who asked the least questions in all wins. If this number is the same, they share the victory.

A person who has been deceived is eliminated. If no code announced is correct, the others continue their investigation. If only one player remains, he wins by default. Avoid revealing the solution to those who need to continue; players who have consulted the solution do not give any more clues.

06A progressive logical example

Here's a mini-theoretical example, created to understand the answers : it is not associated with card numbers Check box. We always write blue, yellow, purple.

Auditor A distinguishes "blue equals 3" and "blue greater than 3". 345Blue 3 would have met the first criterion; therefore, it is not the active criterion. The criterion is "blue above 3". We know that blue is 4 or 5, not which of the two.

Verifier B distinguishes "yellow less than 4", "yellow equal to 4" and "yellow greater than 4". If the same proposition 345 receives yes from B, the secret criterion is "yellow equal to 4". Here equality effectively specifies the yellow value.

A C auditor may require that the violet be matched. If an independent deduction also imposes purple greater than 3, the only possible value between 1 and 5 is 4. This last crossing is a deduction, not an additional question asked free of charge to the machine.

The next round, a blue proposal 4 would make it possible to distinguish certain remaining assumptions, according to the real auditors of the problem. Before choosing this question, write what would mean yes and no: a question whose two answers do not change anything does not help your inquiry.

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07Victory, solo and cooperation

In competition, the correct announcement in the first run where someone normally finishes the game, with the selection to the total number of questions. There is no card score or points for an isolated number found. The objective is the entire code.

In solo or in cooperation, uses a single sheet of notes and solves the problem in as few rounds and questions as possible. On the official website, the function "Did you beat the machine?" allows you to compare the performance with the result of the machine. To many, discuss the assumptions instead of hiding the answers: this distinguishes this mode from the competitive mode. The commercial material allows up to four people, even if you can also think collectively around a sheet according to a family agreement.

A problem already solved can be used to explain an idea, but it is no longer a new investigation for the person who knows his code. Putting the cards at the right locations and erasing the check marks at the end.

08Frequent errors

• Mix the blue, yellow and purple values when writing the code.
• Use a wrong Check card or place it backwards.
• Change the proposal after the first question of the handle.
• Consolidate "satisfied the criterion" and "accord exactly with the code".
• Interpret a no as direct information on the three digits.
• Forgetting to note a question, which distorts the separation.
• Consult the solution too early and then continue to help others in competition.

09Tips for Investigation

Separate the facts and assumptions. A note "A: blue > 3 certain" is more useful than a code surrounded without explanation. Bar only the assumptions actually incompatible with the answer received.

Do not start questioning an auditor whose criteria you already know, unless you control a material error. Once the rule is discovered, it is your reasoning that must apply it to future codes.

Choose a proposal that divides the remaining possibilities. When yes and no leave you exactly the same candidates, look for a better question. At first, play the introductions without rushing; the economy of questions comes after the correctness of the deductions.