386.—­A TRICK WITH DICE.

[Illustration]

Here is a neat little trick with three dice.  I ask you to throw the dice without my seeing them.  Then I tell you to multiply the points of the first die by 2 and add 5; then multiply the result by 5 and add the points of the second die; then multiply the result by 10 and add the points of the third die.  You then give me the total, and I can at once tell you the points thrown with the three dice.  How do I do it?  As an example, if you threw 1, 3, and 6, as in the illustration, the result you would give me would be 386, from which I could at once say what you had thrown.

387.—­THE VILLAGE CRICKET MATCH.

In a cricket match, Dingley Dell v.  All Muggleton, the latter had the first innings.  Mr. Dumkins and Mr. Podder were at the wickets, when the wary Dumkins made a splendid late cut, and Mr. Podder called on him to run.  Four runs were apparently completed, but the vigilant umpires at each end called, “three short,” making six short runs in all.  What number did Mr. Dumkins score?  When Dingley Dell took their turn at the wickets their champions were Mr. Luffey and Mr. Struggles.  The latter made a magnificent off-drive, and invited his colleague to “come along,” with the result that the observant spectators applauded them for what was supposed to have been three sharp runs.  But the umpires declared that there had been two short runs at each end—­four in all.  To what extent, if any, did this manoeuvre increase Mr. Struggles’s total?

388.—­SLOW CRICKET.

In the recent county match between Wessex and Nincomshire the former team were at the wickets all day, the last man being put out a few minutes before the time for drawing stumps.  The play was so slow that most of the spectators were fast asleep, and, on being awakened by one of the officials clearing the ground, we learnt that two men had been put out leg-before-wicket for a combined score of 19 runs; four men were caught for a combined score or 17 runs; one man was run out for a duck’s egg; and the others were all bowled for 3 runs each.  There were no extras.  We were not told which of the men was the captain, but he made exactly 15 more than the average of his team.  What was the captain’s score?

389.—­THE FOOTBALL PLAYERS.

“It is a glorious game!” an enthusiast was heard to exclaim.  “At the close of last season, of the footballers of my acquaintance four had broken their left arm, five had broken their right arm, two had the right arm sound, and three had sound left arms.”  Can you discover from that statement what is the smallest number of players that the speaker could be acquainted with?

It does not at all follow that there were as many as fourteen men, because, for example, two of the men who had broken the left arm might also be the two who had sound right arms.

390.—­THE HORSE-RACE PUZZLE.