THE CABINET MAKER’S PUZZLE.
[234.] A cabinet maker has a circular piece of veneering with which he has to veneer the tops of two oval stools; but it so happens that the area of the stools, exclusive of the hand-holes in the centre and that of the circular piece, are the same. How must he cut his veneer so as to be exactly sufficient for his purpose?
THE ARITHMETICAL TRIANGLE.
| 1 | |||||||
| 2, | 1 | ||||||
| 3, | 3, | 1 | |||||
| 4, | 6, | 4, | 1 | ||||
| 5, | 10, | 10, | 5, | 1 | |||
| 6, | 15, | 20, | 15, | 6, | 1 | ||
| 7, | 21, | 35, | 35, | 21, | 7, | 1 | |
| 8, | 28, | 56, | 70, | 56, | 28, | 8, | 1 |
Write down the numbers 1, 2, 3, &c., as far as you please in a column. On the right hand of 2 place 1, add them together and place 3 under the 1; the 3 added to 3 = 6, which place under the 3, and so on; this gives the second column. The third is found from the second in a similar way. By the triangle we can determine how many combinations can be made, taking any number at a time out of a larger number. For instance, a group of 8 gentlemen agreed that they should visit the Crystal Palace 3 at a time, and that the visits should be continued daily as long as a different three could be selected. In how many days were the possible combinations of 3 out of 8 completed?
Method: Look down the first column till you come to 8, then see what number is horizontal with it in the third column, viz., 56. (For the method usually adopted for working out calculations like the above, see Doctrine of Chance.)
[235.] Why is a pound note more valuable than a sovereign?