Cutting Logs and BagelsEarly Elementary CircleNovember 20th, 20111. How many pieces will you get if you cut a log with 3 cuts?What about 10 cuts?What about 27 cuts?What about 2011 cuts?Do you notice a general pattern?PIECES = CUTS±_____12. How many cuts do you have to make to cut a log into 3 pieces?What about 10 pieces?What is the general rule here?CUTS = PIECES±______23. Now suppose that you have 2 logs. You cut each log some number oftimes so that all together there are 4 cuts.(a) how many pieces do you get?(b) Given that the number of cuts is 4, does the number of pieces youget depend on the number of cuts on each log?4. You still have 2 logs and make some cuts on both of them. The totalnumber of cuts is 10. How many pieces do you get?35. Looking at questions 3 and 4, do you see a general pattern with thenumber of pieces and cuts when you have 2 logs?PIECES = CUTS±______6. What happens when you cut three logs? Investigate this idea, and seewhat general pattern you can find.47. The Tin Man says that he got 10 pieces after making just five cuts. Howmany logs did he start with?8. The Tin Man says that he can also get 10 pieces of wood by makingonly three cuts. Do you believe him? If yes, how can he do it? If no,why not?59. No you have a bagel instead of a log. If you cut it with 3 cuts, howmany pieces do you get? (1 cut is cutting the bagel from the hole to theedge. Thuse, one cut DOES NOT create two pieces.)10. What if you cut it with 5 cuts?10 cuts?What happens if you make just one cut? What is the general rule here?Does it work for any number of cuts?611. Suppose you have 2 bagels. You cut each bagel some number of timesso that all together there are 4 cuts. How many pieces do you get? Doesit depend on how many cuts you choose to put on each log?12. What happens if you take two bagels and make a total of 7 cuts onthem. How many pieces can you get? Can you come up with a generalrule for the number of pieces you can get by cutting two bagels?713. Now suppose you have 3 bagels and you make 3 cuts. How many piecescan you get?14. Dorothy says she got 4 pieces after making 3 cuts. How many bagelscould she have had to start