It is the fraction 6⁄9 which is unchanged when turned over, and which, when taken thrice, and then divided by two becomes 1.
10.
When the three gamblers agreed that the loser should always double the sum of money that the other two had before them, and they each lost once, and fulfilled the conditions, remaining each with eight sovereigns in hand, they had started with £13, £7, and £4 as the following table shows:—
| A | B | C | |
|---|---|---|---|
| £ | £ | £ | |
| At starts | 13 | 7 | 4 |
| When A loses | 2 | 14 | 8 |
| When B loses | 4 | 4 | 16 |
| When C loses | 8 | 8 | 8 |
11.
Tom’s sum, which his mischievous neighbour rubbed almost out, is reconstructed thus:—
| 3 | 4 | 5 | 3 | 4 | 5 | |||||
| * | * | 3 | 7 | |||||||
| * | * | * | * | 2 | 4 | 1 | 5 | |||
| * | * | * | * | 1 | 0 | 3 | 5 | |||
| * | * | 7 | 6 | * | 1 | 2 | 7 | 6 | 5 | |