Intellect Sharpeners

New Zealand Herald, Volume LXX, Issue 21562, 5 August 1933, Page 5 (Supplement)

Intellect Sharpeners

BT T. L. EKITON

GAME OF CRIBBAGE

Three men "X," " and "Z" sat down to play a " three-corner" game of cribbage, that is each man played for himself, and there was a small financial interest on the result decided by points. The s only money involved in the game was first placed upon the table, the total sum, in J5 coins being 125., all in New Zealand silver currency. Each man had the same number of coins. " X " had the largest sum and "Z" the smallest, the latter .having as much less than "Y " as "X " had more than the last named player. The result of the game as determined by the respective points gained and lost, was that " Z " won sixpence from " X," and also sixpence from " Y." The first mentioned two men sottled their accounts by each exchanging two coins with tho other, "Z"and "Y" squaring their differences by each exchanging one coin. The men then possessed thoir original number of coins, " X." having then the same sum as "Y " started with, and " Z " a similar amount to that held by "X" at tho commencement of the game. The question is that if " X " began with coins of two denominations only, and " Y " and " Z " with coins of three denominations each,. what sum did they -then have respectively, and how was each amount made up? This puzzle is one for the armchair. Some of the details given are not essential, being included for* intellect-sharpening purposes. AN OLD QUESTION

" Kaituna " has Bent an inquiry concerning an old puzzle that is always cropping up and causing much controversy as to tho possibility or otherwise of a solution. Tho problem has in recent years appeared in more modern dress, the well-known mathematician, H. Dudeney, having submitted it under the designation of " Water, Gas and Electricity," and it is probable that it is in this form " Kaituna " .has seen it. Three houses in a row on one side of a street are each requiring the services mentioned, the depots of which are in a row in three separate establishments directly opposite tho houses in question. How can the water, gas and electricity be laid to each residenco without any drain or pipe crossing another. The correspondent adds that he and his friends have been trying for some time to find how this can be done. He thinks that perhaps some reader of this column would enlighten him. To those who have not examined the puzzle before, it is suggested that an interesting half-hour may well- be spent with a diagram showing the posiions thus; W G E H H H And with a pencil draw such lines as may be thought would solve the problem. - ""TWO FOB THE ARMCHAIR

If a man has £450 left of his annual "<■ salary, after paying his yearly insurance premium and Government taxation, both payments being equivalent to 2s. in the pound of his salary, how much does he pay in insurance premiums if the sum is in the ratio of one to four to the amount paid in taxation, and what is his aurkual salary ?

A woman purchasing eggs was told bv the storekeeper that the price was threepence a dozen higher if the customer picked the eggs from the box herself. She accepted the terms of purchase, and personally selected a certain quantity for which, she paid .'is 6d at the higher rate ihentioned. Had she been willing to let the seller • take the eggs at random from tho , box, she would have received three more eggs for the money she had paidCan the reader say without using a pen or pencil, how many eggs she got for tho 3s 6d. TRANSFERRING CREDIT

There are four separate accounts operated upon in a certain business which are opened and closed daily, and i it is the practice in the courso of a day's business to transfer credits from * one to another so that none will show less than £lO credit. It may be accepted that the four accounts are in an even > number of pounds which will almost " bring the calculation within the category of "armchair" puzzles. Let us call the respective accounts " W," " X," " Y " and " Z " and assume that at ! the commencement of business on a certain day all of them are in credit, i and that the sum in " Y " account iai £2O more than that in " Z " account, In the course of the day, the following; "V transfers are made. One quarter olf-'n-" " Y's " account to " X's " credit,, . ' making the combined "W " }. u " ■ and " Y " accounts equal to that in " X " and " ZJ> Then one third of - < the sum in " WV account is transferred 'to " X's " credit, then ono > quarter of " X's" credit to " Y," 0110 fifth of " Y's" credit then to accoun i " Z," and finally one-quarter of tho - ' sum then in "X's" account is transferred in equal shares to each of thu • • ! three others. If then the four accounts have equal sums to their credits, can the reader say what amounts were in L tho respective accounts at the com- .>7.': mencement of >hat day's business? . "V LAST WEEK'S SOLUTIONS " Restoration " Sum.—Divisor 1111, dividend 11,108,889, and the quotient i, ' r 9999. -

Two For the Armchair.—Forty-nine and 56. (2) There would bo 81 posts required. Solution of second armchair problem published July 22: Sixteen boys, one receiving Is 9d and the others, Is 3d each. Alphabetical Sum.—Tho numerical (J equivalent of the letters R S T U • .< V W X Y Z arc 6 2 7 8 1 5 i ■ 3 and 9 respectively. Six is the digit not used, that number being the square root of two loss than tho numerical equivalent YU. ' Fusible Metal.—Eight-ninths of a ton alloy, 202 2-91b. of lead, 'and •16 2-31b. of tin. . Alphabetical Addition.— ;J 39,567 .§■' ; ' 2,487 64,310

106,364 The alphabetical total is ALMRMO, nsfr ALARMO. ANSWERS TO CORRESPONDENTS , " Mark " A .capital budget; thanks! " Curious " —Another glance at t!io question is suggested. 'A Ipliabctical''—Alternative jnotho ds could bo adopted, but tho results cannot vary. - " RE.S."—Sorry, but problem seint is one by tho Rev. E.F.0., " The Solitary Seven." t " C.K.G." —It is-calculated that tbo . ;. 7 - Kim's light travels the 98,000,000 miles to the earth in eight minutes—mately, of* course. >. " EN. ZED."—It .is a good point and ; opens up a new idea of treating, tlio , question, but the trouble "is that, not being mathematical, it .may lead on<J, if (°llow«<l blind),.