THE BASICS OF HOW TO PLAY AND THE FOUR BEGINNING STRATAGIES

THE OBJECT OF THE GAME

Using a series of logical deductions, find a four-digit number based on a set of clues that are given. 

To solve the puzzle, you must identify the 4 correct digits in the answer and have them in the correct positions.

There are no math skills needed, just simple logic.

 

Sample picture of a puzzle.

When you compare the clues and use the information provided by the Pica’s and the Centro’s, you will be able to solve the puzzle. 

  • The puzzles use the numbers 1 through 9. Zero is not used.
  • A number cannot be used more than once in an answer.

THE PARTS OF THE PUZZLE

Let’s take a look at a puzzle and get familiar with each part of it.

CLUES:  The main part of the puzzle are the CLUES.         In this puzzle there are 3 clues, labeled a, b, and c.

Each CLUE/ROW has four numbers.  Some (or none) of these numbers may be Pica’s or Centro’s.

POSITIONS:  Each number in a CLUE is in a POSITION. 

There are 4 POSITIONS.   1st, 2nd, 3rd and 4th

# of PICA’S:  (Pica is defined on the next page)

Shows how many of the numbers in that clue are Pica’s.

# of CENTRO’S:  (Centro is defined on the next page)

Shows how many of the numbers in that clue are Centro’s.

ANSWER:  This is where you write the answer!

SQUARES with 1 thru 9:  A visual aid to track information as you go through the steps to solve the puzzle.

THE DEFINITION OF A PICA AND A CENTRO

In this example the answer has been filled in, which is 8743

A PICA represents a number in the clue that is in the answer, but is in the wrong position.

Note the letter “P” to indicate Pica in the example.

A CENTRO represents a number in the clue that is in the answer, AND is in the correct position.

Note the letter “C” to indicate Centro in the example.

Look at the example and compare the position of a Pica or Centro in a clue with the position of that number in the answer.   A good example is to compare the 3 in clue c, to the 3 in clue a or clue d.

Notice in the example that there can be more than one Pica or Centro in any given clue.  (Or there can be zero!)

Do you understand the difference between a Pica and a Centro?

This is the key to solving the puzzles!    Position is important!

HOW TO SOLVE A PUZZLE

Using logic, you will go through a series of steps to identify the numbers in the answer and their correct position.

  • The most common approach is to take information from one clue and compare it to information in another clue. Using various strategies, you will be able to identify numbers that cannot be in the answer or that must be in the answer.
  • Repeat this process until you can solve the puzzle. As you identify numbers that are/aren’t in the answer, you will be able learn more information from the clues.
  • It is very helpful to mark the puzzle as you go. This will visually help you to see the next step.
    • Put an X over numbers that can’t be in the answer
    • Circle the numbers that are in the answer.
    • Put a small “p” next to numbers that are Pica’s.
    • Put a small “c” next to numbers that are Centro’s.
  • You should never have to guess!
  • A few puzzles have a short title or comment. That may be a hint for you or just a bit of trivia from me.
  • It may be possible to solve a puzzle in different ways or a different order. Find your own way!

Zero Pica’s and Zero Centro’s Strategy

Let’s take a look at a puzzle and see how to solve it.  (Or you can try it on your own first!).  

STEP 1

  1. One of the most helpful ways to start a puzzle is when one of the clues has Zero Pica’s and Zero Centro’s.

When you see this, it means all of the numbers in that clue are NOT in the answer!

  1. In this puzzle, clue a has zero Pica’s and zero Centro’s. This means that the numbers 1, 3, 7, and 5, are NOT in the answer.   (If any of them were in the answer, there would be at least one Pica or one Centro).
  2. At this point you mark your puzzle with what you have learned. Put an X over every 1, 3, 7, and 5 in the puzzle, no matter which clue they may be in.

The puzzle will now look like this.

Marking the puzzle as you go is very helpful.  It makes it easier to see the next steps to take!

STEP 2

With this added information, you can now learn more from clue b and clue c.

In clue b, you can see the 7 and 5 are not in the answer.  You know that two of the numbers in this clue must be Centro’s.    So, by simple process of elimination, you know that the 4 and the 2 represent the two Centro’s in clue b.

Do you remember what a Centro is?  This means the number is in the correct position.

So, the 4 belongs in the 3rd position in the answer, and the 2 belongs in the 4th position in the answer.

Circle the 4 and the 2. 

 

The puzzle now looks like this.

STEP 3

Now take a look at clue c.

Can you identify which two numbers are the Centro’s?

  1. Because the 1 and the 3 have already been crossed out, you can see the 9 and the 6 must be the two Centro’s in clue c.
  2. Because they are Centro’s, the 9 belongs in the 1st position and the 6 in the 2nd The puzzle is now solved!
  3. The correct answer is 9642.

 

Take a look at the next two puzzles and see if you can solve them using the “zero Pica’s and zero Centro’s” strategy.

 

Total of Four Pica’s and Centro’s

STEP 1

  1. In clue a there are four Pica’s. When the number of Pica’s plus the number of Centro’s in one clue equals four, then you know that each number in the clue is in the answer.
  1. Next, you need to determine the correct position for each number.
  2. Look at the position of the 8 in clues a, b & d. Note that each clue has 4 Pica’s and Zero Centro’s.  
  3. In clue a, the 8 can’t be in the 1st In clue b, the 8 can’t be in the 2nd position.   In clue d, the 8 can’t be in the 4th position.  (Because these are all Pica only clues.  No Centro’s)
  4. The 8 goes in the 3rd position, the only position still open.

With our new information added, the puzzle now looks like this.

STEP 2

  1. Find the positions where the 2 must be a Pica. Make sure to only use the clues that have zero Centro’s. (Clue c has two Pica’s and two Centro’s)
  2. The 2 can’t be in the 2nd position based on clue a. It can’t be in the 1st position based on clue b.  It can’t be in the 3rd position based on clue d.
  3. The 2 must go in the 4th position

STEP 3

  1. Repeat this process with the 4 using clues a, b & d.
  2. What position does the 4 belong in?
  3. It is in the 2nd (and is a Centro in clue c)

STEP 4

  1. Only one spot is left. The 1 is in the 1st
  2. The answer is 1482!

Now try these two puzzles on your own using this strategy.

 

Clues with only Centro’s (zero Pica’s) Strategy

Remember what the Pica’s and Centro’s tell you about the position of a number in a clue.

 

STEP 1

  1. The number 6 is in the 2nd position in clue a.
  2. The number 6 is in the 1st position in clue c.
  3. Now notice:
    • Clue a has zero Pica’s and two Centro’s.
    • Clue c has zero Pica’s and one Centro.

This means whichever number(s) in clue a and clue c that are in the answer, they must be in the correct position. Because the number must be a Centro. (There are no Pica’s in either clue).  Got it?

  1. Next, compare what clue a and clue c tell you about the number 6.

  1. If 6 was in the answer, based on clue a, it would have to be in the 2nd (It’s a Centro’s only clue)
  2. However, based on clue c, the 6 would have to be in the 1st (It’s a Centro only clue)
  3. When you compare the two clues, you can deduce that the 6 CANNOT be in the answer. Clue a and clue b are incompatible. Both can’t be true if 6 was in the answer.

To summarize this strategy

WHEN The same number is in different positions in multiple clues.

IF Both clues have only Centro’s (zero Pica’s).

THEN The number is not in the answer

The puzzle now looks like this.

STEP 2

  1. Can you find another number that fits the criteria used in Step 1? (Same number, Centro only clues, and the number is in a different position in each clue.)
  2. Look at clue a and clue c.
    • The number 9 is in the 3rd position in clue a.
    • The number 9 is in the 4th position in clue c.
    • Clue a has zero Pica’s and two Centro’s
    • Clue c has zero Pica’s and one Centro.
  3. 9 CANNOT be in the answer. Those two clues are incompatible if 9 was in the answer. 
  4. Put an X over the 9’s and see if you can finish the puzzle.

 

The puzzle now looks like this.

STEP 3

(if you need help finishing the puzzle.)

  1. Look at clue a. It has two Centro’s. You know the 6 and the 9 are not in the answer.
  2. By process of elimination, the 3 and 7 are the Centro’s. The 3 is in the 1st position and the 7 is in the 4th position.

STEP 4

Look at clue d.  You should have the 3 circled.  There is only one Centro in the clue.   This tells you that the 4, 2 and the 8 are not in the answer.  Put an X over them in all the clues.

STEP 5

Look at clue c.  The 6, 2 and 9 are not in the answer.  5 must be the one Centro in the clue and goes in the 2nd position

STEP 6

Look at clue b.  1 must be in the answer. It goes in the 3rd position, the only one open.  The answer is 3517.

Here are two puzzles that use this strategy.

Hint: first look for clues that have only Centro’s (zero Pica’s), then look for the same number in different positions.

 

 

Clues with zero Pica’s in one clue and zero Centro’s in another clue strategy.

 

STEP 1

  1. For this strategy, you look for a number that is in the same position in different clues.
  2. Let’s use the 6 in clue a, in the 3rd position, and  the 6 in clue d, also in the 3rd
  3. Clue a has zero Pica’s and two Centro’s. This means the 6 would have to be a Centro (i.e. in the correct position) in the 3rd position, if it is in the answer.
  4. Clue d has 1 Pica and zero Centro’s. This means the 6 would have to be a Pica in the 3rd position (i.e the wrong position), if it is in the answer.
  5. Do you think the 6 is in the answer?

The answer is No. The 6 CANNOT be in the answer.  Clue a and clue d are incompatible.  It can’t be a Pica in one clue and a Centro in another clue if it is in the same position

STEP 2

  1. Next, take a look at this puzzle and see if you can find another number where this strategy can be used. Remember to look for a number in the same position.
  2. Look at the 7 in clue c and the 7 in clue d. It is in the 2nd position in both clues. (You could also use the 8 in clues b & c too!)
  3. Clue c has zero Pica’s and two Centros. Clue d has 1 Pica and zero Centro’s.
  4. Based on clue c, if 7 was in the answer it would be Centro and belong in the 2nd position. However, based on clue d, the 7 would be Pica and couldn’t be in the 2nd position.
  5. 7 CANNOT be in the answer.The clues are incompatible.

               

The puzzle now looks like this.

To summarize this strategy:        

WHEN the same number is in the same position in multiple clues.

IF one clue has zero Pica’s, and the other clue has zero Centro’s.

THEN the number is not in the answer.

This strategy may sound similar to the previous strategy. 

But they are different.  You don’t need to memorize them, just remember what the Pica’s and Centro’s tell you in each clue, pay attention to the position and think logically.

Clues with either zero Pica’s or zero Centro’s are helpful.

See if you can finish this puzzle from here.

Here are two puzzles that start with this strategy.   Remember to mark as you go.

Hint:  first look for numbers in the same position.  Then check for zero Pica’s in one clue and zero Centro’s in the other clue.

 

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