Puzzles
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This is an old math puzzle given in my own made up narrative.
A column of (Type E)Bots is moving slowly forward at
exactly one mile per hour. Bot End-E who is at the
rear of the column gives a message to a courier Bot, Speed-E,
who has just arrived by his side, the message is to be
given to Bot Head-E who is at the front of the column
ten miles ahead. Speed-E sets his controls to be back
at End-E’s side in exactly one hour and a constant
speed in MPH to achieve this.
When Speed-E is at the side of bot Head-E the message is
instantly transferred as Speed-E instantly reverses and
travels back to End-E on time.What was the constant MPH speed that Speed-E set?
Anyone with an answer should save it and post it on Tuesday 30th September
this means all answers will be seen together when the Keymaster puts them ALL up at
the same time (to be determined by the Keymaster!)HARRY 28-SEP-25 NEWS PUZZLE – REPOSTED HERE WITH MY OWN NARATIVE ENDING
I got it from Raymond Chandler, you know the guy? Writer, gumshoe, loved a mean street. Anyway, turns out he loves a good puzzle too, and this one is more than good. He heard I liked coin flipping mysteries (see this news item from last year) and thought I might like this one. See what you make of it!
The night was black and wet, and the cave was worse. I went in looking for shelter and found a troll instead. He was ugly the way a fist is ugly—big, raw, and ready to break something. Behind him sat a mountain of coins. Thousands. Gold on one side, silver on the other. Half with the gold sides grinning at me, the others had turned their pale cheeks up. The troll laid it out flat. “Two piles. Same number of silver facing up in each; miss, and you’re dead.” Then he killed the torch. The dark came down heavy, thick enough to choke on. I couldn’t see. Didn’t matter. Guessing was suicide . . .
===================== THE STORY CONTINUED = MY VERSION . . .
After what seemed like an eternty, not becuase of my trying to figure it out but because of the stupid amount of coins, I said “Hey ugly, you can put the light on now and start inspecting ’em its getting late” He grabbed hold of me and I thought I was in for a beating, turned out he was making sure I didn’t run off while he examined the piles. To my relieve the troll kept his word and let me go, I scurried out calling back “Tell your next victim that there is an even amount of coins you loser”.
I wondered if I should return later with a friend a powerful searchlight, a shotgun and a wheelbarrow. Would you?############ ANSWER DO NOT READ THIS UNLESS YOU WISH TO ############
Short Answer without proof:
Split the coins into two equal piles and flip all the coins in one pile.
Solution can be done in darkness, and without guessing.Another (difficult?) math puzzle given in my own made up narrative.
A contest where YOU are one of the contestants.
The quizmaster host has brought six contestants to a stronghold building
having just one door, he tells them that “there is a pile of gold coins inside
and that it costs nothing to enter via the door but it will cost one coin
in a slot to exit. There are instructions inside telling you what to do, one
of you will not be going in and that person needs to be very good at maths,
as a correct answer from her/him will determine if you all win, so get to and
sort yourselves out and then we will begin, oh and you all must be honest and
accurate if you wish to win.”YOU are chosen to be maths master!
The host asks each of the other five contestant in turn to enter the door.
The first contestant went in, the door closing behind, read the notice and conformed.
As did the second, third, fourth and fifth.When all five had had their turn the host then instructs:
“Now all five of you are to enter together and take an equal share of the coins.”
He hands them a bucket each.When they are finished the host says
“I can see there are no coins left over so you were all honest and accurate in all your
dealings. However to keep all your gold coins, each worth £100, your chosen player
needs to answer one question. One of you can tell the chosen math person how many
coins you have in your bucket and what the message inside instructed you to do.”One of them steps up to YOU and says “204 coins and the message inside was
‘take one coin for the door, then count the remaining coins and remove one fifth of them
and put them into the hole nearby, then leave’.”The host then gives YOU a bucket and instructs the other five to each put 35 coins into
it from their own bucket, to be your share of the reward if YOU win it for everyone.The host then handed YOU a card with a question on it.
and said “No one else is to see it or help you, please write your answer on the card.”The question on the card read:
‘What is the smallest possible number of coins that the original pile in the building
contained?’Would your answer win £17,000 for each of you?
No pressure but the other five keep looking at their bucket then back at you!Put up your answer and lets find out!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Extra questions you may like to compute:1] How many coins in total were put into the hole?
2] If the question on the card had read:
‘What is the smallest possible number of coins that the original pile in the building
contained if there was one coin left over after the five shared the remaining pile’
Then what would your answer be?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~What are the differents answers for this puzzle?
SORRY JUST NOTICED AN ERROR IN MY POST
I gave:
The host then gives YOU a bucket and instructs the other five to each put 35 coins into
it from their own bucket, to be your share of the reward if YOU win it for everyone.It should be 34 coins like so:
The host then gives YOU a bucket and instructs the other five to each put 34 coins into
it from their own bucket, to be your share of the reward if YOU win it for everyone.It does not alter the answer but gives unequal winning amounts to contestants and spoils the story
@F6EXB_the_frenchy
There is one main answer to give
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
and two others only if you want to.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~@ByteInBits,
Sorry, I was asking about your puzzle about robots in columns (post #104162), for which no answers were posted. But the moderators did not approve the messages in the order they arrived.#104162 Robot question answer.
>What was the constant MPH speed that Speed-E set?
Let the speed of Speed-E be v, the speed of the column be w and the duration of the outward and return journeys be t1 and t2 respectively.
We know:
t1 + t2 = 1
and that Speed-E catches Head-E when
v.t1 = 10 + w.t1
and that Speed-E returns to End-E when:
v.t2 = v.t1 – w
In this case w = 1 and the above simplify to:
v.t1 = 10 + t1
and
v.t2 = v.t1 – 1
Solving for t1 we get:
t1 = (sqrt(101)-9)/2
and v = 1/(sqrt(101)-10) approximately 20.499 mph.
@F6EXB_the_frenchy [fyi it is a single column of bots]
Maybe no one posted an answer for the E-Bots puzzle and so the keymaster has nothing to put up!
If anyone has an answer they are still welcome to put it up (forget the date instruction)
I posted a reply, but it hasn’t been approved yet.
That is good, hope you got it right. Maybe we need more replies, so patience is needed.
I will not give answer until much much later then all can see if they are correct or not
same will apply to the coin puzzle or any others I post.Speed must go to the front of the column, so 10 miles, and then return to the rear, another 10 miles.
The time t1 of the outward journey is the distance divided by its speed. t1 = 10 / (v-1). (v-1 because the column is moving in the same direction).
The return time t2 is the distance divided by its speed. t2 = 10 / (v+1). (v+1 because the column is moving in the opposite direction).
t1 + t2 = 1 (one hour)
t1 + t2 = 10 / (v-1) + 10 / (v+1) = 1
[10(v+1) + 10(v-1)] / (v+1) * (v-1) = 1
(10v + 10 + 10 v -10) =( v² – 1)
20v = (v² – 1)
v² – 20v – 1 = 0
v = 10 + sqr(101) (the positive result)Translated with DeepL.com (free version)
>and v = 1/(sqrt(101)-10) approximately 20.499 mph.
I see I made an error in evaluating the numerical value of the velocity. I should have said 20.0499 mph.
If you, like me, are required to carry out numerous arithmetic calculations, I can recommend Thomas de Colmar’s Arithmometer, as exhibited at The Great Exhibition of 1851. I have found it of great benefit in reducing errors in basic arithmetic calculation. I should make better use of it.
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Card and Paper Puzzle Answer
Although it may seem surprising, the minimum square side is 50mm. The square is cut and then the newspaper is folded along the diameter of the square hole and the circle offered up to the hole inside the fold. By gently moving the opposite sides of the hole down the circle, the paper forms a collapsed pyramid shape and the two cut edges form a straight line of total length 100mm. At this point the card circle will slide through.
Card and Paper Puzzle
I cut a 100 mm diameter circle out of stiff card a square hole from the centre of a sheet of newspaper. What is the smallest side length of the square hole which will allow the card circle to pass through the hole in the paper without bending the card and without tearing the paper? For the purposes of the puzzle, we can ignore the thickness of the card.
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