# Fun and Fundamentals of Mathematics by J.V.Narlikar - M.Narlikar By J.V.Narlikar - M.Narlikar

This booklet introduces basic principles in arithmetic via intersting puzzles. scholars, from age12 upwards, who're tired of regimen classwork in maths will take pleasure in those puzzles so as to sharpen will sharpen their logical reasoning. it's designed to arouse an curiosity in arithmetic between readers between readers within the 12-18 age crew.

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7 Standing room only! When will the Earth become so crowded? 36 FUN AND FUNDAMENTALS OF MATHEMATICS 3. Show that the the infinity of points on the unit interval, on a straight line, is of the same magnitude as the infinity of points in a unit square. 4. The story of the hare and the tortoise is well known. The hare lost because he took a long nap on the way. But here is an argument that shows that even if the hare were running fast he could not overtake the tortoise, provided the tortoise was ahead to begin with.

3, we have used rectangular coordinate axes OX,OY and OZ to identify the directions of the edges of the main cube. Taking the slices parallel to the OXY plane, we have three sets of nine tiny cubes. 2, with eight sets of 3 tiny cubes in a row. So in three slices we have 3 x 8 = 24 such sets. Now look at the slices parallel to the OYZ plane. Here too you will have 24 sets of 3 triplet cubes. But not all of them are new. Some were already included in the slices parallel to the OXY plane. These are the sets parallel to the direction OY.

It is easy to see that there are nine of them. Hence, we have only 24 - 9 = 15 new ones to add, thus making the total of 24 + 15 = 39. Next, we add the new sets from the slices parallel to the OXZ plane. Of the 24 sets in these slices, 9 are common with the slices parallel to the OXY plane and 9 parallel to the OYZ plane. So we have only 24 - 9 - 9 = 6 new ones to add, thus bringing the total to 39 + 6 = 45. We are not done yet! There are triplets that lie along the diagonals of the cube. Since there are four such diagonals, the total finally adds up to 45 + 4 = 49 triplets.