Maths Is Fun

question 1 A useful know-how : the Math of Lock-Picking An electronic lock has a circular dial with 4 equally spaced buttons on the rim each controlling a switch. If all 4 switches are in the on position or all in the off position the lock opens. You can attempt to open the lock by simultaneously pressing any number of the buttons. If you are lucky enough to thereby align the switches then the lock opens, otherwise the dial rapidly rotates for one minute. When it comes to rest and you have no way to know which buttons you pressed last time. Can you guarantee that you can open the lock in less than 15 minutes? question 2 Solve this equation by making it to have 2008 answers: X^3+Y^3=Z^2? question 3 Maths is Beauty : Origami Prepare some long thin strips of paper. Lay them on a table in front of you left to right. Mark one end 'top left' so that it can be re-positioned later without difficulty. Take the first strip and fold the left hand end over to meet the right hand end and press down to make a crease. Now take the double right hand end and fold it over to meet the new left hand end (what was the middle). Do another right to left fold, pressing down to produce good creases each time. Unfold the paper and almost flatten it into its original position. Looked at edge on you should see that some of the the creases point upwards U, and some point downwards D. This particular result should be recorded as LRR ---> DUUDDDU. Investigate how the number of D's and U's and more particularly their order is related to the number and order of the L's and R's. Try to form rules which will help you predict the order of U, D for LRRRLLRL.