Part 3 (1/2)
89--ADDING THE DIGITS
If I write the suits, they suit has thus been used a second tiest amount possible under the conditions Now find the ss, pence, and farthings being all represented You need not use it ht is not allowed
90--THE CENTURY PUZZLE
Can you write 100 in the forits once, and only once? The late distinguished French mathe it, and expressed his doubts as to there being any other ways As a matter of fact there are just eleven ways and no more Here is one of theures in the integral part of the nuure there Can the reader find this last form?
91--MORE MIXED FRACTIONS
When I first published my solution to the last puzzle, I was led to attempt the expression of all nu all the nine digits Here are twelve numbers for the reader to try his hand at: 13, 14, 15, 16, 18, 20, 27, 36, 40, 69, 72, 94 Use every one of the nine digits once, and only once, in every case
92--DIGITAL SQUARE NUMBERS
Here are the nine digits so arranged that they form four square nuether so as to forle square nuest possible?
93--THE MYSTIC ELEVEN
Can you find the largest possible nuht a digit) that can be divided by 11 without a remainder? Can you also find the smallest possible number produced in the same way that is divisible by 11? Here is an exait 5 has been oits and is divisible by 11, but it is neither the largest nor the smallest number that ork
94--THE DIGITAL CENTURY
1 2 3 4 5 6 7 8 9 = 100
It is required to place arithures so that they shall equal 100 Of course, you ures Can you give a correct solution that ens, and (2) the fewest possible separate strokes or dots of the pen? That is, it is necessary to use as few signs as possible, and those signs should be of the sins of addition and multiplication (+ and ) will thus count as two strokes, the sign of subtraction (-) as one stroke, the sign of division () as three, and so on
95--THE FOUR SEVENS
[Illustration]
In the illustration Professor Rackbrane is seen de one of the little posers hich he is accusto his pupils off the beaten tracks he is the better able to secure their attention, and to induce original and ingenious ht He has, it will be seen, just sho four 5's ns so as to represent 100 Every juvenile reader will see at a glance that his example is quite correct Nohat he wants you to do is this: Arrange four 7's (neither ns so that they shall represent 100 If he had said ere to use four 9's we ht at once have written 99+9/9, but the four 7's call for rather enuity Can you discover the little trick?
96--THE DICE NUMBERS
[Illustration]
I have a set of four dice, not ures, as shown in the illustration Each die, of course, bears the nuood many, different numbers As represented they make the nuure nu the saure more than once in any number), ill they all add up to? You are allowed to turn the 6 upside down, so as to represent a 9 I do not ask, or expect, the reader to go to all the labour of writing out the full list of nuh for such wasted energy Can you get at the answer in any other way?
VARIOUS ARITHMETICAL AND ALGEBRAICAL PROBLEMS
”Variety's the very spice of life, That gives it all its flavour”
COWPER: _The Task_ 97--THE SPOT ON THE TABLE
A boy, recently hoive his father an exhibition of his precocity He pushed a large circular table into the corner of the room, as shown in the illustration, so that it touched both walls, and he then pointed to a spot of ink on the extree
[Illustration]
”Here is a little puzzle for you, pater,” said the youth ”That spot is exactly eight inches from one wall and nine inches from the other Can you tellit?”
The boy was overheard to tell a friend, ”It fairly beat the guv'nor;” but his father is known to have re in his head in a minute I often wonder which spoke the truth
98--ACADEMIC COURTESIES
In a certain mixed school, where a special feature was oodThere were twice as irl, to every boy, and to the teacher Every boy irl, and to the teacher In all there were nine hundred bowsNow, can you say exactly how many boys there were in the school? If you are not very careful, you are likely to get a good deal out in your calculation
99--THE THIRTY-THREE PEARLS
[Illustration]
”A man I know,” said Teddy Nicholson at a certain fa of thirty-three pearls The est and best of all, and the others are so selected and arranged that, starting from one end, each successive pearl is worth 100pearl From the other end the pearls increase in value by 150 up to the large pearl The whole string is worth 65,000 What is the value of that large pearl?”
”Pearls and other articles of clothing,” said Uncle Walter, when the price of the precious gem had been discovered, ”remind me of Adam and Eve Authorities, you may not know, differ as to the number of apples that were eaten by Adam and Eve It is the opinion of some that Eve 8 (ate) and Adam 2 (too), a total of 10 only But certain ured it out differently, and hold that Eve 8 and Adaators think the above figures entirely wrong, for if Eve 8 and Adam 8 2, the total must be 90”
”Well,” said Harry, ”it seeiants in those days, probably Eve 8 1 and Adaive a total of 163”
”I am not at all satisfied,” said Maud ”It seeether consu,” insisted Mr Wilson, ”for I consider that Eve 8 1 4 Adaet a total of 8,938”
”But, look here,” broke in Herbert ”If Eve 8 1 4 Adae Eve, surely the total ested that they ht let the matter rest He declared it to be clearly what mathematicians call an indeterminate problem
100--THE LABOURER'S PUZZLE
Professor Rackbrane, during one of his ra a deep hole
”Good ,” he said ”How deep is that hole?”
”Guess,” replied the labourer ”My height is exactly five feet ten inches”
”How oing twice as deep,” was the answer, ”and then round”
Rackbrane now asks if you could tell how deep that hole would be when finished
101--THE TRUSSES OF HAY
Farmer Toe to weigh before delivering thehed them two at a tihts in pounds were 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 Noas Farures how ly? The reader ht to be told ”which pair is which pair,” or soive the five correct weights?
102--MR GUBBINS IN A FOG
Mr Gubbins, a diligentThe electric light happened to be out of order and he had to e as best he could with two candles His clerk assured hith one candle would burn for four hours and the other for five hours After he had been working so had lifted, and he then noticed that what reth of as left of the other
When he got hoood puzzle, said to hi those two candles were burning to-day I'll have a shot at it” But he soon found hi than the atmospheric one Could you have assisted hi?
103--PAINTING THE LAMP-POSTS