This guy has a collection of five groups of animals comprising mammals, birds, snakes, spiders and insects. Now assume that usually animals have one head, mammals have four legs, birds have two legs, snakes have zero legs, spiders have eight legs and insects have six legs. However, our dude has picked up some freak beasts like a mammal with three legs, a bird with two heads, a snake with three heads, a spider with seven legs and an insect with four legs. Given the following information determine how many of each group of animals the weirdo has in his keep.
(1) There are a total of 100 heads and 376 legs; (2) Each group has a different quantity of animals; (3) The most populous group has 10 more members than the least populous group; (4) There are twice as many insect legs as there are bird legs; (5) There are as many snake heads as there are spider heads.
THROUGHPUT
(The yellow-bellied ornery toothpick problem was actually a bit of a cheat but I’m happy to say at least one person still managed to suss it out. Curses on him!)
Regarding your toothpick mania, I could manage to make 500 though not 200. The two pieces on the top can be considered close enough to be taken as a single bar, what is left is ‘s’ under a bar. According to Roman numerals ‘s’ denotes fraction 0.5 and bar represents vinculum. That is the number is multiplied by 1000. Hence it will mean 500. But 200, that screwed me. Bitu Nayak, 2998b2nayak2998@gmail.com
Place the toothpicks in the form that you have given in the question, on a glass table. When seen from the other side, the diagram will be 2T, which stands for 2 tons = 200, in colloquial, British English. -- Agnimitra Srivatsav, agnimitra234@gmail.com
Believe it or not, from the solution given, I had thought that if one of the dots were considered as a decimal point it could be the answer. And I did consider sending it in but felt that it was too simple to be the solution and didn’t want to stick my neck out. Too simple, because the given solution handheld us up to 1/5 and I felt that .200 as the solution was a no brainer. -- Balagopalan Nair K, balagopalannair@gmail.com
(The second problem was: “Can anyone devise a general procedure so that ‘n’ persons can cut a cake into ‘n’ portions in such a way that everyone is satisfied he or she has at least 1/n of the cake -- preferably leaving no excess bits?”)
Let anyone be chosen at random to cut the first piece. He should cut what, in his judgment, is 1/nth of the cake. Whether indeed he can have it is decided by the remaining n - 1 guys (if he has cut an unduly large share, he can’t have it, so he has an incentive to be fair). Then another person is chosen from among the remaining n - 1 guys and procedure is repeated till only two persons are left. One of them cuts the piece and the other takes it. If at any stage, the cutter can’t have the piece cut, then all those people who remain are pooled again and the remaining cake is also pooled to repeat the procedure. -- Prof S Manikutty, manikuti@iima.ac.in
(The last one was: “A is standing 100 metres south of B. Now B starts travelling due east at speed x, whereas A starts travelling at speed 2x in a direction that always faces where B is at that moment. How much distance would B have travelled when he meets A?
Let the starting points of A and B be a and b respectively and the meeting point be c. By connecting these points we get a right angled triangle abc where ac (the hypotenuse) is 2bc and ab is 100 (metres). Using the Pythagorean theorem we get the equation (2bc)square = (bc)square + 10000. By solving this equation we get bc = 57.735 metres. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com (Yes Sangita, rakshasangita77@gmail.com and S V S Sivam, svssivam@yahoo.com you aced it too!)
BUT GOOGLE THIS NOW
1. Consider the above problem again. Instead of the speeds of B and A being x and 2x respectively, if their speeds were equal (say x), then A would never be able to meet B. In that case, what would then be the closest distance between A and B?
2. Check out the lowly chapatti. The two halves are always of unequal thickness; one thin like paper, the other thicker. It’s the same thing with deep-fried poories. Ever wondered why? Or how to make them with halves of equal thickness?
Mukul Sharma
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)