PAST
SOLUTIONS TO THE DAILY BRAIN TEASER BY E-MAIL CLUB
#500 TO #599
THE
SOLUTIONS
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Number 599
The boy's age was ten and his sister's four.
Number 598
Ten
Number 597
Add IV turned upside down below VI and you get XI.
Number 596
The canvas must be 10 in. in width and 20 in. in height; the picture itself 6 in. wide and 12 in. high. The margin will then be as required.
Number 595
Margaret Marshall went to the bank and to the grocery store, Doris Price went to the bank and to the hardware store, Ethel Torrey went to the butcher shop and the grocery store, and so did Lucille Winters.
Number 594
Father and child; or paternal uncle/aunt and nephew/niece.
Number 593
Mitchell teaches French and history, Morgan teaches biology and English, and Myers teaches economics and mathematics.
Number 592
There were six men representing four lodges.
Number 591
Since there are no childless
couples every family must have at least one girl, either as an
only child or as the sister (required by the second fact) of such
boys as there may be. Thus there must be at least as many girls
as families. But then, since there are more boys than girls, the
total number of children must necessarily be more than twice the
number of families, that is, more than the total number of adults
since there are just two adults per family. This contradicts the
first fact of the report and constitutes the inconsistency for
which the census taker was reprimanded.
Number 590
Abstemiously
Number 589
The next day, or tomorrow.
Number 588
#1=Haste makes waste.
#2=A fool and his money are soon parted.
Number 587
Part 1
3,121
Original Bag.....Monkey's
Share.....Purloined Portion
3121.................................1....................624
kept by #1
2496.................................1....................499
kept by #2
1996.................................1....................399
kept by #3
1596.................................1....................319
kept by #4
1276.................................1....................257
kept by #5
1020.................................1.....240 divided among all
Part 2
15,621
Original Bag.....Monkey's
Share.....Purloined Portion
15621...............................1...................3124
kept by #1
12496...............................1...................2499 kept
by #2
9996.................................1...................1999
kept by #3
7996.................................1...................1599
kept by #4
6396.................................1...................1279
kept by #5
5116.................................1....1023 divided among all
Number 586
Yes. He took as much time for the second half of his trip as the whole trip would have taken on foot. So no matter how fast the train was, he lost exactlt as much time as he spent on the train. He would have saved 1/30 of the time taken by walking all the way.
Number 585
There is exactly as much water in
the wine pitcher as there is wine in the water pitcher.
Regardless of the proportions of wine and water which have been
transferred, if both pitchers originally held equal volumes of
unadulterated liquids and both are eventually left the equal
volumes of mixtures, then equal amounts of wine and water must
have been transferred.
This old brainteaser also forms the basis of a perplexing card
trick: The performer and the spectator are seated opposite each
other at a table. The performer turns 20 cards face-up from a
pack of 52 cards. The spectator is asked to shuffle the pack so
that the reversed cards are randomly distributed, then to hold
the pack out of sight beneath the table and to count off 20 cards
from the top. These 20 cards are passed, under the table, to the
performer.
Having taken the 20 cards, the performer continues to hold them
beneath the table, and tells the spectator: "Neither of us
knows how many reversed cards there are in this pack of 20.
However it is likely that there are fewer reversed cards in the
pack of 20 than there are in the pack of 32 which you are
holding. Without looking at my cards, I am going to turn some
more face-down cards face-up in an attempt to equalize the number
of reversed cards in my packet with the number in yours."
The performer then fiddles with his packet of cards under the
table, making out that he can feel the difference between fronts
and backs. After a few moments, he brings them into view and
spreads them on the table. When the face-up cards are counted, it
turns out that their number is exactly the same as the number of
face-up cards in the spectator's packet of 32. What he's done, of
course, is just turn his entire stack of 20 cards over.
Number 584
Red
Number 583
The number of letters contained in each numeral word.
Number 582
ALL THAT GLITTERS IS NOT GOLD.
Number 581
He makes eight cigarettes and smokes them, leaving eight ends from which he makes two more cigarettes, a total of ten.
Number 580
There are 215 different dates in this century complying with the conditions, if we include such cases as 25/4/00. The most fruitful year was 1924, when we get the seven cases: 24/1/24, 12/2/24, 2/12/24, 8/3/24, 3/8/24, 6/4/24, 4/6/24. One has only to seek the years containing as many factors as possible.
Number 579
100
330
505
077
099
----
1111
Number 578
There are two solutions with
numbers less than ten: 3 and 5, and 7 and 8.
The general solution to this problem is as follows:
Calling the numbers a and b, we have:
a² + b² + ab= p=/a-mb/²=a²-2amb+b²m².
:b+a=-2am+bm²,
:b=a(2m+1)/m²-1
in which m may be any whole number greater than 1, and a is
chosen tointhebrationaL The general values are a = m² - 1 and b
= 2m + 1.
Number 577
Twice 4 added to 20 is 28. Four of these (a seventh part) were killed, and these were those that remained, for the others flew away.
Number 576
The place is Venus, where a day is longer than a year. Venus takes 225 Earth days to go around the sun but it takes 243 Earth days too rotate on its axis. In any event, it is unlikely that many people would like to go there for either period; the avg. temp is around 885°F, and their are thick clouds of sulphuric acid. If you know of a better solution please post in the FORUM!
Number 575
I'd save four hours, not counting recovery time!
Number 574
Sally was short by 6.75 inches. She needed 180 inches, but the owner gave her only 165 plus 5 percent of that.
Number 573
ADMIRER and MARRIED
Number 572
They were both women's teams!
Number 571
There are 5,040 ways of arranging the childern, and 720 different ways of placing a girl at each end. Therefore, the chances are 720 in 5,040, or 1 in 7. Or, which is the same thing, the chances are 1 in 6 in favor, or 6 in 1 against there being a girl at both ends.
Number 570
The farmer's seventeen horses were to be divided in the proportions 1/2, 1/3, 1/9. It was not stated that the sons were to receive those fractions of seventeen. The proportions are thus 9/18, 6/18, and 2/18, so if the sons receive respectively 9, 6, and 2 horses each, the terms of the legacy will be exactly carried out. Therefore, the rediculous old method described does happen to give a correct solution.
Number 569
Sixty days and fourty days!
Number 568
Hilda's blunder amounted to multiplying by 49, instead of by 409. Divide the error by the difference (328,320 by 360) and you will get the required number-912.
Number 567
On the odd side of the street the house must have been No.239, and there were 169 houses on that side. On the even side of the street the house must have been No.408, and there were 288 houses.
Number 566
Brown's number must have been 84, and there were 119 houses. The numbers from 1 to 84 sum to 3,570 and those from 1 to 119 to 7,140, which is just double, as stated.
Number 565
Arthur could do the work in 14
34/49 days
Benjamin in 17 23/41 days
Charles in 23 7/31 days
Number 564
It depends
on the reason for the scales' imbalance. If the pans are of
unequal weights, the grocer's solution will work; but if the arms
of the scale are of unequal lengths, it will not, and the grocer
will lose. This can be shown algebraically as follows:
Let a and b be the unequal lengths of the arms of the scale, x
the fixed weight, and y and z the amounts of, say, sugar weighed
out. Then ax = by and bx = az, so the weight of sugar dispensed
is:
{a/b +b/a}
which is greater than 2x. For
a/b + b/a>2;a(2)-2ab+b(2)>0;and(a-b)(2)>0
are equivalent statements when a and b are distinct positive
quantities.
It can also be explained in terms of physics. While adding a
compensating weight to a light pan will bring the scales
permanently into balance, adding a compensating weight to the
side with a short arm will only put the scales into momentary
balance. The combined effect of a long arm and weight added to
that side (in the form of goods, for instance) will be to
increase the imbalance progressively, so that ever more
compensation is needed.
Number 563
x= value of the coat. After seven
months the butler is entitled to 7x/12 + 700/12. However, he
receives only $20, therefore, 5x/12 must compensate for the
difference between $700/12 and $240/12 ($20) therefore,
5x = 460
and x = $92
Number 562
Let x be the length of the bolt.
Then x/3 + x/4 + 8 = x. This reduces to:
4x+3x+96=12x, or5x=96
x=19.2 yards.
Number 561
Mahogany
Number 560
As in fact you are starting with two lentils on the second day, you save one day, therefore the answer is 29 days.
Number 559
The second, because x/30 + x/40
is greater than 2x/35
Proof: x/30 + x/40 = 7x/120 or 245x/4200
2x/35 = 240x/4200
Number 558
Because he is a security guard, that works at night. If he was sleeping and dreaming, means that he was incompetent and the company was unsafe.
Number 557
Ten problems.
Let x be the number of correct solutions, and y be the number of
incorrect solutions.
Then: x+y = 26
and 8x-5y = 0
From first equation y = (26- x)
8x-5(26-x)= 0
or 8x= 130-5x
x= 10
Number 556
Because my red-haired colleague is male.
Number 555
The oldest boy asked Daddy for another dollar, making $18. He took $9.00, gave the middle brother $6.00, and gave the baby $2.00. Then he returned the extra dollar to Daddy.
Number 554
One hundred fifty minutes is two and a half hours.
Number 553
My friend is too short to reach the buttonin the elevator for the fifteenth floor--he can reach only as high as ten. On the way down, the first--floor button is easy for him to reach.
Number 552
1 ton
250 centimeters
3 raised to the 5th power
zero degrees Centigrade
inches in a kilometer
-40 degrees Centigrade and -40 degrees Fahrenheit are equally
cold.
Number 551
a. brag, garb
b. revel, lever
c. paws, swap
d. laud, dual
e. mood, doom
f. warts, straw
g. step, pets
h. debut, tubed
i. snip, pins
j. evil, live
Number 550
On average half the women will bear
a girl first, and half will bear a boy, so on first births, the
numbers of boys and girls will be equal. The women who bore a
girl will then have no more children, while the half who bore a
boy will continue to bear, having as second children, half boys
and half girls, so that the balance of boys and girls is
preserved. Among the third children to be born within families,
there will also be a balance of boys and girls, and so on. The
fact is that the number of families which consist of only one
girl, which amounts to no less than one half of all families,
will exactly balance the much smaller number of families
containing several boys followed by a girl. Indeed, this amounts
to no more than the fact that
1/2 = 1/4 + 1/8 + 1/16 +....
This solution assumes that the ratio of births of boys to girls
is indeed one to one; the ratio actually favours boys very
slightly, but this ratio in itself will never produce the surplus
that the King requires, and his ingenious scheme will be of no
help at all.
Number 549
a. Nevada b. Maine c. Maryland d. Washington e. Minne-sota f. Rhode Island g. Indiana h. Pennsylvania i. Rhode Island j. South Carolina
Number 548
The only other four digit number
complying with the conditions is 9801.
98 plus 0l is 99, and 99 squared is 9801.
Number 547
The bicycle moves backwards. However, the pedal moves forwards, relative to the bicycle, so that the pedals as a pair are rotating, as would be expected, in the opposite direction to that required to move the cycle forwards.
Number 546
This is an example of the
'pigeon-hole' principle. Consider one million boxes, numbered
consecutively from 0, for the completely bald, to 999,999 for
those people (who might just exist according to the information
given) who have that many hairs on their head.
Place one slip for each person in the United Kingdom into the box
corresponding to his or her number of hairs. Then at least one
box must contain fifty slips of paper, corresponding to at least
fifty people with that same number of hairs on their head.
Number 545
Very
simple, my dear Watson," the Sultan chuckled. 'As a matter
of fact I expected this good news exactly on that day. My people,
as I suggested before, may be too lazy to organize the shadowing
of their wives for the purpose of establishing their faithfulness
or unfaithfulness, but they have certainly shown themselves
intelligent enough to resolve the case by purely logical
analysis."
"I do not understand you, Great Sultan," said the
vizier.
"Well, assume that there were not fourty unfaithful wives,
but only one. In this case, everybody with the exception of her
husband knew the fact. Her husband, however, believing in the
faithfulness of his wife, and knowing no other case of
unfaithfulness (about which he would undoubtedly have heard) was
under the impression that all wives in the city, including his
own, were faithful. If he read the proclamation which stated that
there are unfaithful wives in the city, he would realize it could
mean only his own wife. Thus he would kill her the very first
night. Do you follow me?"
"I do," said the vizier.
'"Now let us assume," continued the Sultan, "that
there were two deceived husbands; let us call them Abdula and
Hadibaba. Abdula knew all the time that Hadjibaba's wife was
deceiving him, and Hadjibaba knew the same about Abdula's wife.
But each thought his own wife was faithful.
"On the day that the proclamation was published, Abdula said
to himself, 'Aha, tonight Hadjibaba will kill his wife.' On the
other hand, Hadjibaba thought the same about Abdula. However, the
fact that next morning both wives were still alive proved to both
Abdula and Hadjibaba that they were wrong in believing in the
faithfulness of their wives. Thus during the second night two
daggers would have found their target, and two women would have
been dead. "I follow you so far," said the vizier,
"but how about the case of three or more unfaithful
wives?"
"Well, from now on we have what is called mathematical
induc-tion. I have just proved to you that, if there were only
two unfaithful wives in the city, the husbands would have killed
them on the second night, by force of purely logical deduction.
Now suppose that there were three wives, Abdula's, Hadjibaba's,
and Faruk's, who were unfaithful. Faruk knows, of course, that
Abdula's and Hadlibaba's wives are deceiving them, and so he
expects that these two characters will murder their wives on the
second night. But they don't. Why? Of course because his,
Faruk's, wife is unfaithful, too! And so in goes the dagger, or
the three daggers, as a matter of fact."
"O Great Sultan," exclaimed the vizier, "you have
certainly opened my eyes on that problem. Of course, if there
were four unfaithful wives, each of the four wronged husbands
would reduce the case to that of three and not kill his wife
until the fourth day. And so on, and so on, up to forty
wives."
"I am glad," said the Sultan, "that you finally
understand the situation. It is nice to have a vizier whose
intelligence is so much inferior to that of the average citizen.
But what if I tell you that the reported number of unfaithful
wives was actually forty-one?"
Number 544
Achilles would reach the tortoise at 1,111 1/9 meters. If the race track is shorter than this, the tortoise would win. If it were exactly this size, it would be a tie. Otherwise Achilles will pass the tortoise.
Number 543
The boy picked a pebble out of the hat and, before they had a chance to examine it, dropped it, apparently accidentally, where it was lost among the pebbles on the ground. He then pointed out to the king that the color of the dropped pebble could be ascertained by checking the color of the one remaining in the hat.
Number 542
5 1/3 (5 minutes 20 seconds)
Speed downstream is 1/2 km. per minute. Return speed is 1/4
kilometer per minute. Therefore the current makes 1/8 of a
kilometer difference per minute.
Consequently, the boat speed is 3/8 of a kilometer per minute,
which translates into 5 1/3 minutes for the 2 kilometers in still
water.
Number 541
Twenty-four pieces of gum.
Number 540
$5762.50
Number 539
Monday
Number 538
chest, calves, muscle, feet,
temples, pupils, heel, nails, lashes, arms
Number 537
Take one bill from the envelope marked $15 (which is a wrong marking). Say it would be a $5 bill. Now you know the other left in the envelope is also a $5 bill. You also know now that the envelope labelled $20, since it is labelled wrong, cannot contain $20. You already know which is the correct $10 envelope, hence the one labelled $20 has to contain $15. The remaining envelope has to be the one with $20 in it. Use the same procedure if you should pick the one with the two $10 bills in it.
Number 536
If there are m men, then
clearly 1-m is a solution, albeit a negative one, since, if you
take one away (the one for the monkey), and then divide the
remainder by m, it will mean that each man gets - 1. If one man
then takes his portion and puts the rest back, then there will be
1 -m again. And the process can be repeated.
Now, if there are m men, there will be m+ 1 share-outs, and
therefore, besides 1 -m being a solution, there will also be
solutions at intervals of:
1 m+m(m+l) and
1 m+2 x m(m+l) and
1 m+3 x m(m+l)
and at every multiple of m(m+1)
But clearly, the least positive solution will be 1 -m+m(m+1)
In our problem, m=6, therefore the minimum number of coconuts is:
1-6+6(7th power)=279,931 coconuts.
Number 535
Consider the puzzle with statements 1-5 only, and denote '2 is true' by 2T, and so on. 2T implies 5T implies 4F (since 4T, 5T would make 4F). 4F implies two consecutive true statements, which is impossible. Therefore 2F. 2F implies 4T (since 4F would have to be true), which implies 3F and 5F. Thus iF 2F 3F 4T 5F, and the answer to this shortened puzzle would be '4 alone'. But adding the statement 6, if 6T then its removal would affect the answer, and therefore 6F. Thus since 6F, the answer cannot be 4 alone. 2T can again be ruled out making 2F. Hence again 4T so 3F and 5F. The only combination left which works and does not give the answer '4 alone' is 1T 2F 3F 4T 5F 6F.
Statements 1 and 4 are true.
Number 534
He asks either of the warders, 'Does the warder who is guarding
the road that leads to freedom tell the truth?' If the warder he
asks replies 'Yes', he goes through that warder's door. If the
warder replies 'No', he walks to freedom through the other door.
Number 533
All they had to do was tilt the
barrel on its bottom rim till the water was just about to pour
out. If the barrel is exactly half full, the water level at the
bottom of the barrel should just cover all the rim. That way half
the barrel is full of water; the other half is air space. If the
water arnply covers the bottom rim, the barrel is more than half
full; if the bottom is not fully covered, the barrel is less than
half full.
Number 532
a. The fiendish spectre
haunts the manor each night
b. Never trifle with strange beasts
c. Genuine antique dealers seldom deal in replicas
d. A recipe if perfect lists all the ingredients
e. A tornado can cause alarming results when it hits a town
f. In general, granite rocks are the hardest ones
Number 531
OTT F F S SEN... being the initial letters of One, Two, Three, Four, Five, Six, etc.
Number 530
The two keen sportsmen started at their fitness club, one on the cycling machine and the other on the walking ma-chine. After half an hour of indoor exercise they went for a run. The distance from A to B is 2 miles.
NUMBER 529
The buses are evenly spaced along the road in both directions. The man notices buses at the rate of 30 an hour. Because he is moving towards one "stream" of buses and away from the other, he sees more buses in one direction than the other (20 to 10), but if he were stationary he would see 15 an hour traveling each way. The buses ffierefore leave the terminal at 4-minute intervals.
Number 528
If two widows had each a son, and each widow married the son of the other and had a daughter by the marriage, all the relationships will be found to result.
Number 527
Colonel Cholomondely-Snaithworth-Jones was lying, and the explorers knew it. There are no wild tigers at the headwaters of the Nile, or anywhere else in Africa. Liars like the colonel come along only every four years.
Number 526
2688
NUMBER 525
The fallacy is exposed when you use the argument of the problem to prove that any two horses are of the same colour. Removing each of the horses in turn only leaves the other one horse, and the set of N - 1 horses which are all of the same colour as each other, and the same colour as the horses removed, has one member. If only it were possible to conclude that any pair of horses were the same colour, then it would indeed - and very obviously - follow that any three, four, five, etc., horses were of the same colour.
NUMBER 524
Gus had ten pigs, Joe had fourteen pigs.
NUMBER 523
The most likely total is 13. For every way in which you could end up with a total of 14 or more, there is a way of ending up with 13: all you have to do is to throw one less, and this is certainly possible because you cannot first exceed 12 and arrive at a total of 14 or more by throwing a 1. Therefore the number of ways of reaching 13 is at least as great as the number of ways of reaching any higher total. But their are also ways to first exceed 12 and reach 13, for example by starting with 12 and throwing a 1, which do not have any matching throws for higher totals. Therefore there are more ways of getting to 13 and the probability is greatest that your total will be 13.
NUMBER 522
Defying, fighting, hijack, monopoly, querist, understudy
NUMBER 521
Jim
NUMBER 520
It makes two complete rotations.
NUMBER 519
The poorest shot, the Baron of Rockall, has the best chance of surviving. Lord Montcrief, the one who never misses, has the second best chance. Because the baron's two opponents will aim at each other when their turns come, his best strategy is to fire into the air until one of the others is killed. He will then get the first shot at the survivor, which gives him the advantage.
NUMBER 518
Sunday
NUMBER 517
a. Guyana |
b. America |
c. Afghanistan |
d. Jordan |
e. Indonesia |
f. New Zealand |
g. Hungary |
h. Great Britain |
i. Philippines |
NUMBER 516
80 minutes.
NUMBER 515
1. Ashes.
2. A haircut.
3. The rifles are long enough already.
4. Lunch, dinner, and supper.
5. An unbrella.
6. Normal; your fingers should be equally spread over
two hands.
7. Six dozen dozen; it is 12 times as much as half a
dozen dozen.
8. You cannot get down from a camel. You get down from a duck.
9. They were tinned tomatoes.
10. There are more of them.
Rate your score on the following
scale:
8 to 10 correct=Whiz
6 to 7 correct=Smart
3 to 5 correct=Fair
2 or less=Look at answers again take test over, score better, I
would hope! LOL!
NUMBER 514
Milligan stuffed animals. The man in the garage had heard that Milligan was a famous local taxidermist and thought that he ran some kind of taxi service!
NUMBER 513
The train takes 30 seconds to travel 1km, plus 3 seconds for the complete train to pass any point, making a total of 33 seconds.
NUMBER 512
CHECKED stood out because it was the only word which could be read directly from the office stamp.
NUMBER 511
Four. The sentence contains three spelling mistakes, plus the false clam that it only contains one mistake, making a total of four mistakes.
The second question, paradoxically, cannot be answered. It contains only two spelling mistakes but clams to contain three mistakes; therefore that clam is wrong and it actually contains three mistakes--except that if it contains three mistakes then the claim that it contains three mistakes is correct, and so it only contains the two spelling mistakes, in which case.....!
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