86.
If, when a man met a beggar, he gave him half of his loose cash and a shilling, and meeting another gave him half what was left and two shillings, and to a third half the remainder and three shillings, he had two guineas at first.
87.
The clerk who has two offers of work from January 1, one from A of £100 a year, with an annual rise of £20, and the other from B of £100 a year, with a half-yearly rise of £5, should accept B’s offer.
The half-yearly payments from A (allowing for the rise), would be 50, 50, 60, 60, 70, 70, etc., etc.; and from B they would be 50, 55, 60, 65, 70, 75, etc., etc., so that B’s offer is worth £5 a year more than A’s always.
88.
If I have a number of florins and half-crowns, but no other coins, I can pay my tailor £11, 10s. in 224 different ways.
This can be found thus by rule of thumb: Start with 0 half-crowns and 115 florins. Then 4 half-crowns and 110 florins. Add 4 half-crowns and deduct 5 florins each time till 92 half-crowns and 0 florins is reached.