The moral of this puzzle is twofold:  (1) Never take things for granted in attempting to solve puzzles; (2) always remember All Fools’ Day when it comes round.  I was not writing of any gardener and cook, but of a particular couple, in “a race that I witnessed.”  The statement of the eye-witness must therefore be accepted:  as the reader was not there, he cannot contradict it.  Of course the information supplied was insufficient, but the correct reply was:  “Assuming the gardener to be the ‘he,’ the cook wins by 4 ft.; but if the gardener is the ‘she,’ then the gardener wins by 109 ft. 4 in.”  This would have won the prize.  Curiously enough, one solitary competitor got on to the right track, but failed to follow it up.  He said:  “Is this a regular April 1 catch, meaning that they only ran 6 ft. each, and consequently the race was unfinished?  If not, I think the following must be the solution, supposing the gardener to be the ‘he’ and the cook the ‘she.’” Though his solution was wrong even in the case he supposed, yet he was the only person who suspected the question of sex.

429.—­PLACING HALFPENNIES.

Thirteen coins may be placed as shown on page 252.

430.—­FIND THE MAN’S WIFE.

There is no guessing required in this puzzle.  It is all a question of elimination.  If we can pair off any five of the ladies with their respective husbands, other than husband No. 10, then the remaining lady must be No. 10’s wife.

[Illustration:  PLACING HALFPENNIES.]

I will show how this may be done.  No. 8 is seen carrying a lady’s parasol in the same hand with his walking-stick.  But every lady is provided with a parasol, except No. 3; therefore No. 3 may be safely said to be the wife of No. 8.  Then No. 12 is holding a bicycle, and the dress-guard and make disclose the fact that it is a lady’s bicycle.  The only lady in a cycling skirt is No. 5; therefore we conclude that No. 5 is No. 12’s wife.  Next, the man No. 6 has a dog, and lady No. 11 is seen carrying a dog chain.  So we may safely pair No. 6 with No. 11.  Then we see that man No. 2 is paying a newsboy for a paper.  But we do not pay for newspapers in this way before receiving them, and the gentleman has apparently not taken one from the boy.  But lady No. 9 is seen reading a paper.  The inference is obvious—­that she has sent the boy to her husband for a penny.  We therefore pair No. 2 with No. 9.  We have now disposed of all the ladies except Nos. 1 and 7, and of all the men except Nos. 4 and 10.  On looking at No. 4 we find that he is carrying a coat over his arm, and that the buttons are on the left side;—­not on the right, as a man wears them.  So it is a lady’s coat.  But the coat clearly does not belong to No. 1, as she is seen to be wearing a coat already, while No. 7 lady is very lightly clad.  We therefore pair No. 7 lady with man No. 4.  Now the only lady left is No. 1, and we are consequently forced to the conclusion that she is the wife of No. 10.  This is therefore the correct answer.