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For example red and blue: Red Red Blue Blue Result 1: no pegs: red and blue are not in the code Result 2: one white or black peg (let's suppose a white peg). Either red or blue is in the code once. Blue Blue Blue Blue will give you a peg if it's blue, or no pegs if it's red (let's suppose no pegs). In the example we now know there's a red pin, and that it's in the 3rd or 4th spot (as we got a white pin at Red Red Blue Blue). Finding it will be discussed in the next strategy (in one step: Red Green Green Green ). Result 3: more pegs (lets suppose 2 white pegs). Just as Result 2, we can try Blue Blue Blue Blue to know how many pins were blue (lets again assume zero). Now it's only a matter of finding the pins. In the example, we already know the 3rd and 4th are red pins, as there are 2 red pins, and they are not in the first or second spot (as we have gotten 2 white pegs) You can find a pin by trying each of the locations. As an alternate color, we use colors we haven't tested yet. This way, we not only find the red pin but also additional information about other colors. The following is an example, if you know there's a red pin, but don't know in which one of the four holes it is. It will also give you the amount of green, yellow and pink. Red Green Green Green Yellow Red Yellow Yellow Pink Pink Red Pink Note: If you know the exact amount of reds, you don't need to try the last location: if there's one red pin, and it's not in the first, second or third location, it has to be in the fourth). Result 1: If there are no white pegs, you'll have at least one black peg. That peg indicates the red pin is on the correct location Result 2: If there's one white peg, you know the red pin is on an incorrect place, and that the alternate color isn't in the code Result 3: If there's a second white peg, you know the second color should be on the location where the red pin is. Result 4: If there are one or more black pegs, that indicates that the second color is present. It also gives you the number of pins of that color, and you know it's not on the location where red is (as that would give a white peg), or, obviously, on the location where red ends up being Put one color in the place you know, and the other color in the places you don't know. For example green and yellow, and we know the first pin is red: Green Yellow Yellow Yellow Result 1: no pegs; green and yellow are not in the code Result 2a: a white peg indicates green is in the code, but we don't know the amount (it might be one, but also two or even three) Result 2b: the number of black pegs indicates the amount of yellow in the code (as noted in Strategy 2: knowing the exact amount can save you a step in finding the color) This strategy looks a lot like the previous strategy, but now the amount of white pegs also gives us the amount of that color, the, for example, green and yellow, and we know the first two pins are red: Green Green Yellow Yellow Result 1: no pegs: green and yellow are not in the code Result 2a: a white peg indicates one green is in the code, while 2 pegs indicate there are green are in the code (since there are only 2 unknowns, it's impossibly for there to be three greens) Result 2b: as with the previous strategy, the amount of black pegs indicates the amount of yellow in the code. (as noted in Strategy 2: knowing the exact amount can save you a step in finding the color) In this example, as always, we start with strategy 1 ... (strategy 1) Blue Blue Red Red gives 2 white pegs. So we know there's a red and/or blue present. We want to know which is blue and which is red, so we check: (strategy 1 bis) Blue Blue Blue Blue gives one black peg. This means, we know in the previous answer, there was one blue (and on the wrong spot - so will be 3rd or 4th), and thus also one red (and also on the wrong spot, so will be 1st or 2nd) (strategy 2 (find blue)) Green Green Blue Green gives a white and a black pegs. We tested one of the locations of blue, and as there's a white peg, we know it's not the 3rd peg. As we know it was either the 3rd or 4th peg, we know the 4th peg is blue. The black peg also indicates there's a green peg, but it's not the 3rd spot (as it's a black peg, not a white peg). (strategy 2 (find red)) Red Yellow Yellow Yellow gives a single white peg, so while we know, red is in the first or second spot, we now know it's not in the first spot. So it's in the second location. We also know there's no yellow color The next color we had information over was green - but as we know it's not the third spot, and the second and fourth spot is filled with blue & red, we know it's on the first spot. (strategy 4) Orange Orange Pink Orange Gives a white peg. So, we know the only unknown spot - the 3rd spot - has an orange color (answer) Green Red Orange Blue
Eliminate two colors at the same time (with 4 unknown pins). Find the location of a red, if you know there's at least one red pin, but do not know in what of the holes it should be. Eliminate two colors at the same time (with 3 unknown pins). Eliminate two colors at the same time (with only 1 or 2 unknown pins). Learn from an example.