Quandaries and Queries Garrett Secondary Level questions Student is asking(he's a smart one...) A friend hit me with these questions and won't tell me the answer nor how... please help? I've racked my brain and did all sorts of formulas, but I can't get it to work out... please... What's the next number in this series... 5, 12, 17, 29, 46, ? And this series... 12, 19, 28, 39, 52, 67, ? and these... ocoa, boco, oboc, dobo, odob, ? Hi Garrett, What's the next number in this series... 5, 12, 17, 29, 46, ? 5+ 12 = 19 12 + 17 = 29 17 + 29 = 46 And this series... 12, 19, 28, 39, 52, 67, ? 19 - 12 = 7 28 - 19 = 9 39 - 28 = 11 52 - 39 = 13 67 - 52 = 15 and these... ocoa, boco, oboc, dobo, odob, ? This is more problematic: to get the next word from the previous one, you remove the last letter and add a new letter in the beginning. It looks like the new letter should be o if the letter removed is o; if the letter removed is not o, then the letter added could be the one following the letter removed in the alphabet (so the new word would be codo) or the first letter of the alphabet not yet used (so the new word would be eodo). There may be other possible rules, and I cannot decide which was used to start the sequence. This is also true of the other sequences: there may be many rules which will generate the same first few terms (see this example for instance). The one I indicated seems to be the simplest. Claude Go to Math Central