35.—­JUDKINS’S CATTLE.

As there were five droves with an equal number of animals in each drove, the number must be divisible by 5; and as every one of the eight dealers bought the same number of animals, the number must be divisible by 8.  Therefore the number must be a multiple of 40.  The highest possible multiple of 40 that will work will be found to be 120, and this number could be made up in one of two ways—­1 ox, 23 pigs, and 96 sheep, or 3 oxen, 8 pigs, and 109 sheep.  But the first is excluded by the statement that the animals consisted of “oxen, pigs, and sheep,” because a single ox is not oxen.  Therefore the second grouping is the correct answer.

36.—­BUYING APPLES.

As there were the same number of boys as girls, it is clear that the number of children must be even, and, apart from a careful and exact reading of the question, there would be three different answers.  There might be two, six, or fourteen children.  In the first of these cases there are ten different ways in which the apples could be bought.  But we were told there was an equal number of “boys and girls,” and one boy and one girl are not boys and girls, so this case has to be excluded.  In the case of fourteen children, the only possible distribution is that each child receives one halfpenny apple.  But we were told that each child was to receive an equal distribution of “apples,” and one apple is not apples, so this case has also to be excluded.  We are therefore driven back on our third case, which exactly fits in with all the conditions.  Three boys and three girls each receive 1 halfpenny apple and 2 third-penny apples.  The value of these 3 apples is one penny and one-sixth, which multiplied by six makes sevenpence.  Consequently, the correct answer is that there were six children—­three girls and three boys.

37.—­BUYING CHESTNUTS.

In solving this little puzzle we are concerned with the exact interpretation of the words used by the buyer and seller.  I will give the question again, this time adding a few words to make the matter more clear.  The added words are printed in italics.

“A man went into a shop to buy chestnuts.  He said he wanted a pennyworth, and was given five chestnuts.  ’It is not enough; I ought to have a sixth of a chestnut more,’ he remarked.  ’But if I give you one chestnut more,’ the shopman replied, ’you will have five-sixths too many.’  Now, strange to say, they were both right.  How many chestnuts should the buyer receive for half a crown?”

The answer is that the price was 155 chestnuts for half a crown.  Divide this number by 30, and we find that the buyer was entitled to 5+1/6 chestnuts in exchange for his penny.  He was, therefore, right when he said, after receiving five only, that he still wanted a sixth.  And the salesman was also correct in saying that if he gave one chestnut more (that is, six chestnuts in all) he would be giving five-sixths of a chestnut in excess.