Some original riddles

[Zag]

22 is still unsolved. At least, no one has posted the solution.

Here it is for the new page
------------------------------

22. Find the Fool

Another in my "Rhyming Word Ladder" series. The doggerel is pretty bad in places.

Find all ten words described below.

-------------------

The first word you'll need
is a tool used to snare.
Reverse and add one:
a dwelling filled with fresh air.

Append the letter H
to find a metric sort of part.
Now change N to E to get
a smile, at its heart.

Tack on an 'I N G'
to make a baby's cross to bear.
Remove the center two
and find a golfer's action there.

Add an S and drop the E's:
A painful bite you'll see.
Add one to the end: you will make
penny-pinching, miserly.

First 2 and last 2 out the door,
What's left is really cool.
Only keep first half of that
And now you find the fool.

[Jack_Ian]

net
tent
tenth
teeth
teething
teeing
sting
stingy
in
Zag (Well you did write it didn't you)

[Zag]

In my comment when I posted it on Braingle, I said "I am the fool, after all. Or does it refer to you?"

This next one is ridiculously easy, but I'll bet there will still be plenty of people on Braingle that will find it hard. They aren't all geniuses over there.

Anyway, I wanted to make a "real" riddle, that is, one that is in rhyming verse, the answer is a simple, common thing, and the riddle is based on a metaphor. I'm rather satisfied with this one, even though it is too easy.

Hmmm. I think I like it better if the last stanza as a hint rather than part of the puzzle. This makes it quite a bit more challenging. Please give it a try without looking at the spoiler text, since that's a complete give-away. I'm curious whether people can get it without the hint -- I suspect people here will.

25. A Warrior's Shield

I protect one tiny fighter,
Like plate armor, though somewhat lighter.

No jabs from horrible steel spear
Will mar my ward, my precious dear.

The task we do, it may be slight,
But my enemy and I, we close things tight.

Hint: Even though you may be nimble,
You should use me. I'm a ______.

[Jack_Ian]

Well I didn't get it without the spoiler text. I just found it too open, though if I'd guessed the answer, I would have been relatively certain I was correct and I suppose in the end that's all you need.

I would have needed a subtle hint to point me in the right direction and narrow down my choices.

Something like:
The spears approach in a line.
I protect one but save nine.

referring to "a stitch in time..." and a line of thread

[Zag]

Not a riddle, but a probability teaser that I created and posted on Braingle.

26. Duplicate Lottery Picks

In the Massachusetts Megabucks lottery, six different numbers from 1 to 42 (inclusive) are selected. When you buy a ticket, you can ask for a "quick pick" in which the computer chooses the numbers for you, and you can purchase up to five games on a single ticket. We'll assume that the computer's random number generator is fair, giving each possible combination an equal probability of being chosen.

1. If I "quick pick" for two games, what are the chances that the two games have the same combination of numbers?

2. If I "quick pick" for five games (one five-game ticket), what are the chances that there are two games on that ticket with the same combination?

3 (The toughie). How many five-game quick-pick tickets would I have to buy in order to have a greater than 50% chance of having at least one ticket with two games on it that match exactly?

[raekuul]

1: Low
2: Higher, but still low
3: Too many to turn a profit, unless you hit the jackpot.

[PuzzleScot]

There are 850668 different lines (perms) you could have.
C(42,5) = 42!/(5!(42-5)!) or (42.41.40.39.38) / (5.4.3.2.1)
(Assuming each line is chosen independently, and there are no duplicate checks in the software!)

[Zag]

It looks great, except that you used (42 choose 5) rather than (42 choose 6). Here was my write-up on it, which is essentially the same as yours.

1. 1/5245786. The first game on the ticket will be some combination. Then you just calculate the chances that the second game on the ticket will match it. This number of combinations is (42 choose 6) or

42! / 6! (42-6)! = 5245786

So the chances that they match is 1 over this number.

2. For this sort of problem, where you are asking what are the chances of something happening at least once out of several opportunities to happen, you first calculate the opposite -- the chances of it NOT happening in all the tries -- and subtract from 1. So, what are the chances that the 5 games on the ticket are all different?

We know that there are 5245786 possibilities for any one game. In the first game, we choose one of them. The second game now has a 5245785 / 5245786 chance of being different from that first one. Now the third game has a 5245784 / 5245786 chance of being different from either of the first two; and the fourth has a 5245783 / 5245786 chance of being a new selection. When you have the chances of individual events occurring, and you want to know the chance of them ALL occurring, you just multiply. We multiply the chances of all these events occurring (that is, each choice being different) to get:

(5245785 * 5245784 * 5245783 * 5245782) / 5245786 ^ 4

This equals

0.99999809370925005714289758986902

Remember, this is the chance of all of the games on a five-game ticket being different. So the chance of at least two of them being the same is 1 minus this number, or

0.0000019062907499428571024101309848736

which is a really tiny number.

3. We take a similar approach with this calculation that we took before: figure out the chance of it not happening for N tickets, and subtract that value from 1. Then we set that chance to 0.5 and solve for N.

We already know the chance of it happening in one try: the tiny number above, which, for now, we'll call p. So the chance of it NOT happening in one try is (1-p). The chance of it NOT happening in n tries is (1-p)^n, so the chance of it happening at least once in n tries is [1 - (1-p)^n]. We set this formula to 0.5 and solve for n.

Of course, solving for n is tricky, unless you are comfortable with logarithms. I start with the equation

0.5 = [1 - (1-p)^n]

Simplify
0.5 = (1-p)^n

Take natural logarithm of both sides
ln(0.5) = ln( (1-p)^n)

Use logarithm magic
ln(0.5) = n * ln(1-p)

Divide both sides by ln(1-p)
n = ln(0.5) / ln(1-p)

Plug in the number (which we already know) for p and let the calculator do what it's good at
n = 363610.07359999192796640483226154

which is how many tickets we would have to buy to have a 50% chance of seeing one ticket with a match. Since we can't buy fractional tickets, we round up, to make sure we have a greater than 50% chance.

So we need to buy 363611 five-game tickets to have a better than 50% chance of having at least one ticket on which two games match exactly.

Whew!

[PuzzleScot]

bugger. Schoolboy error choosing 5 instead of 6...

Hey, isn't it amazing how high you can reach when you stand on the shoulders of giants [only joking]

[Zag]

27 With a Lion

Another rhyming word ladder.

First name a man with a lion on his flag.
Drop one: a spot to rest, if you drag.

Reverse and add K: a sound grandfather makes.
Change vowel to I, and blood's what it takes.

Add an L and an E. It makes laughter, you know.
Insert an R: it's not much of a flow.

Drop C and scramble, good order is there.
Lose the last two: what first word might wear.

[PuzzleScot]

I had to be the one to solve this!
SCOT -> COT -> TOCK -> TICK -> TICKLE -> TRICKLE -> KILTER -> KILT
Thanks Zag

[Duke Gnome]

Why does a Scot have a lion on his flag?

[PuzzleScot]

The Lion Rampant is on the Royal Standard of Scotland - see Wikipedia.
You will see it waved as often as the Saltire at Scottish international football matches.

[Zag]

[Zag]

28. A Bargain!

This is another of my rhyming word ladder teasers. You may have to work forward and backward to get all eight words.

A bargain is what I have to offer
as the first for you to create.
Last two swap, then add one:
something to make you late.

Lose the E and scramble:
one a tramp would never marry.
Change last to be EN:
under burden, hard to carry.

Turn N to R and add another:
store food and goods in here.
Change the D to be a G.
You've gotten heavy, dear.

Change first and last to B and S:
strong ships without a keel.
Drop ES but add three more:
now that is quite a deal!


29. Nothing to Everything

And another. This is my most challenging, yet, I think. Seven words.

Start with nothing.

Drop the first and add an N,
to make what you could put cookies in.

Add a letter, then you'll see
what a kind of cloth might be.

Drop last two, turn it about.
Your honesty won't be in doubt.

Change V to T, and add ER
For a good place from which to see far.

Change first to L and you will find
what all else is to the word behind.

Replace the middle, drop last one.
Everything, you have! And now you are done.

[Scurra]

Enjoyed 28, once I found an entrance. And of course made me groan when I got to the end.
_________________
_{still Quiz Olympiad champion. Must get a life.
New definitions: COFFEE - someone who is coughed upon}

[Zag]

[Loki]

Yeah, both of these come nicely full circle.

[Oscar]

I'd been idly thinking about doing something like:
'I'm nothing to a man on <noun> but everything to a man who's <verb>ing, where <noun> = <verb>. What am I?'

But I don't think I'll bother now!

[PuzzleScot]

crack ?

[Lepton*]

I've been following these, and I agree that 29 is quite good. The circle here is especially cool.

[PuzzleScot]

I liked 28 & 29 too. Easy once the hook in has been found..

Here's my first attempt at composing:

30. Ready?

Ready?
Add one and rearrange, if it's all too much.
Add one and rearrange, where things are kept.
Add one and rearrange, it's what I am right now.
Add one and rearrange, you might offer in return!
Drop one and rearrange, your beer might be a red one.
Drop one and rearrange, Am I talking rubbish?
Drop one and rearrange, then it becomes quite sexy.
Drop one and rearrange, then you'll be the favourite...

[PuzzleScot]

Perhaps a hint is required? ->First and last are 3-letters, and rhyme<-

Anyone got a part solution yet?

[Zag]

Thanks for the kind words on 28 and 29. Someone should go ahead and post an answer, now.

For 30, I have to say that I can't seem to get started.

I had thought maybe TRASH for rubbish, but then you have to add two letters to make DRAGHTS for beer (and I'm not sure what the "red" clue means). In any case, then the best I had for sexy was STAR. And, unless you are a huge fan of rodents, I have no where to go for "favourite." So I'm pretty sure that's not it.

.

[Zag]

31. Word Sequence

These words define a sequence.

toll, eagle, limb, evil, very, ____, ...

Which of the following words could fit in the blank?

eager, lair, root, tipple

[Jack_Ian]

31(cont.). lair, ...
contest, drag, jockey, race

[Zag]

Correct!

If it isn't clear, Jack_Ian is now offering four words from which the next person should choose the next word after lair. However, Jack_Ian, none of your words quite fit perfectly. I would suggest "lobe" as a better choice than any of yours. (By this additional criterion, "evil" was not a perfect choice, but it was the best I could find.) So I'll take this one and I'll choose "lobe rather than "race" which is what Jack_Ian intended.

31(cont.) ... very, lair, lobe, ___, ...

Choose from these four to fill in the blank, then offer your own four for the next position.

arbor, bill, riches, tire

[PuzzleScot]

[Loki]

[Loki]

[Oscar]

I think the full list is something like:
set>rest>store>poster>riposte>stripe(as in Red Stripe beer)>tripe>pert>pet
I must admit I was a little confused about some of the 'drop one and rearrange' instructions which didn't actually require rearranging.

[PuzzleScot]

100% Correct Oscar! Well done.

I realised a couple didn't need rearranging, but then is didn't scan so well...
Maybe I should stick to solving puzzles rather than setting them

[Zag]

Answers, since no one posted them.

28.
DEAL: a bargain
DELAY: something to make you late

LADY: would never marry a tramp (This is a reference to the Disney movie, "Lady and the Tramp" in which the title characters do get married in the end.)
LADEN: under burden

LARDER: store food and goods in here
LARGER: heavier

BARGES: strong ships without a keel
BARGAIN: quite a deal

29.
LOVE: In tennis, "love" means nothing.
OVEN: a place you might put cookies (to cook them)
WOVEN: describes some cloth
VOW: Your honesty won't be in doubt.
TOWER: a good place from which to see far
LOWER: Everything is lower than a tower.
LOVE: Love is everything, because if you don't have love, you have nothing.

[Loki]

I'll give this format a shot. This is roughly based on the game played between Choronzon and Dream in Neil Gaiman's Sandman Issue #4, "A Hope In Hell".

Choronzon: I am a LIE, and I hide the truth.

Dream: I am a FACT, I provide solid proof.

Choronzon: I shed my tail, and gain two to become the beastly king who knows no peace.

Dream: I change my tail and become the visage of man to tame the beast.

Choronzon: I rip off my tail and turn around and become black liquid to char your skin.

Dream: I alter my front and accept that skin of color is no sin.

Choronzon: I change my head and become nothing, zero, no fraction.

Dream: I rearrange my body and create compassion.

Choronzon: I absorb one to become that which binds compassion to the cross.

Dream: I change one to hide the corpse for three days’ underground, no loss.

Choronzon: I change my head and rain down storms of ice so fierce!

Dream: I alter one and I am sheltered water which ice cannot pierce!

Choronzon: I change my last two and I am a burning rage in the soul!

Dream: I change my head, and I am that which swallows rage whole.

[PuzzleScot]

Dream: FACT -> FACE -> RACE -> CARE -> CAVE -> COVE -> LOVE
Choronzon: LIE -> LION(?) -> OIL -> NIL -> NAIL -> HAIL -> HATE

Nice.

[Zag]

33. Super Powers!

Such super and terrible powers I have!

Given talk, I follow my target stealthily.
With just a kill, I show talent.
I can turn laughter into a horrible scene of death.
On top, I bring everything to a halt!
And if you give me lip, I'll make sure you can't stand up.

What evil villain am I, to wield such power?

(Rather than give the answer, just give another example of my super power!)

[Scurra]

Alas, as an evil villain, my incompetence also shows through at times...
When I tripped on a step, I tore all my clothes off.
When I tuck my costume into my underpants, I often find myself trapped.
And when I say "I'm all ears", I end up burning myself.
_________________
_{still Quiz Olympiad champion. Must get a life.
New definitions: COFFEE - someone who is coughed upon}

[Zag]

Nice!

[Zag]

Anyone else want to chime in on #31 or #33?

If you've solved one and not the other, then a big hint is that they are very similar.

[ralphmerridew]

#31: ... lobe, arbor, rate, ___, ...
helium, neon, argon, krypton

#33:

I headed for my camp, but a scoundrel was waiting for me.
He noticed the cuff of my shirt, and damaged it, then proceeded to lower his bottom onto my corn, while glaring at me with contempt.