Owt for Nowt

Murgatroyd and his friend Grimshaw were down in the dumps. They were seriously financially embarrassed. “Do you know how we might get owt for nowt?” asked Murgatroyd. “Well”, replied his friend, “this puzzle here is really nowt, but if we sent it to the Sunday Times they might give us summat for it”. “What are you on about?” asked Murgatroyd, “what puzzle?”

“Now then” said Grimshaw, “you take about 20 pieces of card, and you put a letter of the alphabet on each of them. Then, rather like Scrabble tiles, you put a number in the corner. But the number doesn't have to be a whole number, and it can be less than nought. However, just as in Scrabble, if you have more than one of the same letter, every time it appears it's worth the same. So with these 20 or so cards, you spell out the first 17 whole numbers - O,N,E, ONE; T,W,O, TWO and so on. Each time you put down a series of cards you add up the score, and, by gum! it is the same as the number you've spelt out. Take ten for instance; if “T” was to be 8¼, and “E” was 5¾, and “N” was - 4, then the total would be 8¼ + 5¾ - 4, which is 10. “Amazing” said Murgatroyd, “but is there only one way this can be done?” “No” replied Grimshaw, “but if I were to say that there were two sets, each set consisting of four different letters, and with the members of the same set having the same value, you should be able to get a single list of values for each letter”. “I see”, said his friend, but does it mean I can get owt for nowt?” “Well yes it does” was the reply, “N,O,W,T does add up to a positive value, but sad to say, if you went outside Yorkshire the total would be even higher. Yes, you get more if you were to ask what “nought” was worth.”

So, can you say what are the respective values of “nowt” and “nought”?