5 red cards1,2,3,4 and 5 and 4 blue cards 3,4,5 and 6. line them up so that the colours alternate, and so that the number on each red card is a factor of every number next to it. How is it done?

Sony Trinitron sets are of CRT [Caothde Ray Tube] types. The common fault seen in these type of TVs are any one colour predominant on screen wih sound OK. Either red, blue or green colour with some thin horizontal lines at about an inch apart will be seen on the entire screen. This is totally a display card problem, which can be seen pluged onto the picutre tube neck. There are three electron guns for every picture tube, which emits red, blue, and green beams, which in turn illuminates the phosphor on the screen to get that colour. If no emission from all guns, results in a blank screen, ie black screen without any disply at all. The three colour beams together produces proper coloured picture what we see on screen. These three gun's terminals are brought out by pins of the picture tube outside to which video signals are given in appropriate proportion to produce a TV picture. Normally, all these three pins are biased with a voltage of about 170 to160VDC+ve. Take one colour gun, as an example and and let me describe the problem.
Let it be a green gun. These guns are called cathodes of the picture tube. If it gets a voltage with respect to its grid, it will emit electrons according to the voltage applied to it. This is a negative process, that is, as the voltage at this pin drops, its emisson incresses and vice versa. If the emission increase, the colour with respect to that gun also will increase and gets predominant at the screen. So when we see a green predominant screen, there will be less voltage at the green cathode with resepect to the other two. If red colour is predominant, the voltage at red cathode will be less than the other two. If blue colour is predominat, the voltage at the blue cathode will be less than the other two.
We must find out the reason for this fault first. Assume that your Tv has a red predominant screen with some thin lines across it, at about one inch apart of the entire screen, it is clear that the the red cathode voltage is very lower than the other two. the main reason for this fault, normally seen in most of the Sony Trinitron, are loose soldering points either to the picture tube base socket or the resistor connected between the red drive transistor's collector point. Resoldering the most of these points on the base card by applying a little more solder will rectify this probelm. Other possibility is shorted video output transistor of that cathode. A direct short [collector to emitter] of these transistors will drop volatge to very low at that respective cathode of the picture tube, and that colour will be pridominant along with lines. Replacing the transistor will solve the problem. In some cases, the resistor connected to that transistor may have blown out. If so, it should alo be replaced. Whatever the case may be, voltage at the respective cathode that emits colour will be very low with respect to the other two. Find out the reason and rectify it. You can compare the voltages of the other two cathodes with respect to the faulty colur cathode. Cathode pins will be marked on the base card, and can be identified. It is best to pull out the base card from the picture tube neck and place it somewhere a safe place without shorting it with other parts of the TV. You can measure the voltages of these points very easly, without fearing the damge to the picture tube. After all are found Ok, replug the base card and switch on the TV. The set will be alright. In rare cases, chroma IC also can be a reason for this fault. if it is faulty, after a short period after switch on the TV, the IC will overheat and shutdown the entire system.