The proprietor of a ladies' school once received an invitation for one-half of her pupils to attend a flower show, but was a long time before she could decide how to pick out those who ought to be rewarded without hurting the feelings of those left behind. There were thirty pupils in the school, and fifteen were to be taken and the like number left at home. The following plan was the one hit upon:—The pupils were arranged in a row, four intended to go were placed first, five not intended next, and so on, as shown below, the letter A denoting those it was intended should partake of the offered pleasure, the letter B denoting those it was wished to leave out, and they were told when so arranged that the ninth girl, and each succeeding ninth, would be left at home.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| A | A | A | A | B | B | B | B | B | A | A | B | A | A | A | B | A | B | B | A | A | B | B | B | A | B | B | A | A | B |
The counting commenced with No. 1, and went round and round consecutively, each ninth pupil being dropped out, as designated to stay at home. It will be seen that those to be left were dropped out in the following order:—9th, 18th, 27th, 6th, 16th, 26th, 7th, 19th, 30th, 12th, 24th, 8th, 22nd, 5th, 23rd, thus leaving fifteen only.
THE DISHONEST SERVANTS.
Three gentlemen, with their servants, had to cross over a river in a boat in which two passengers only could be transported at one time. The servants were known to have planned to murder and rob one or more of the masters if two servants were left with one master or three servants with two masters. The question to be decided was how these six persons were to cross so that the boat could be returned, and yet so that the servants on either side of the river should not outnumber the masters. The following is one of the several ways in which the difficulty might have been overcome:—Two servants go over first, one returns; two servants go over again, one again returning with the boat; two of the masters next go over, and a master and one of the previously taken servants returns; then two of the masters again go over, and the servant already crossed takes the boat back, leaving the three masters safely crossed; the servants are left to come over in any manner they choose.
LORD DUNDREARY'S FINGER PUZZLE TO COUNT ELEVEN FINGERS ON THE TWO HANDS.
Begin on one hand, and count the ten fingers throughout. Begin next time at the finger last counted in the first round, counting this time backwards—ten, nine, eight, seven, six—then holding up the other hand, say "And five are eleven."
UNIFORM RESULTS OF MULTIPLICATION.
| The digits | 15873 | multiplied by | 7 | give | 111111 |
| „ | 31746 | „ | 7 | „ | 222222 |
| „ | 47619 | „ | 7 | „ | 333333 |
| „ | 63492 | „ | 7 | „ | 444444 |
| „ | 79365 | „ | 7 | „ | 555555 |
| „ | 95238 | „ | 7 | „ | 666666 |
| „ | 126984 | „ | 7 | „ | 888888 |
| „ | 142857 | „ | 7 | „ | 999999 |
| Of course, it would need the digits 111111to make | 777777 | ||||