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Fishing for an Answer
Leadfoot Leroy and Careful Carl went on a fishing trip together.
Since it was a long trip, they split the driving; Leroy drove to the lake and Carl did the driving on the way back.
Their average driving speed for the entire trip was 45 MPH.
(from a puzzle magazine)
========================================
18 is the only number whose digits sum to half its value.
splenda-
I suspect “Dr. Pepper” knows what the “old old software interface” referenced by “squeak” is.
I do not.
d=r*t
distance=rate x time
the distance is the same, back & forth
http://www.theyeshivaworld.com/coffeeroom/topic/the-sefiras-haomar-game/page/4#post-243621
am yisrael chai-
Nice catch!
I hadn’t realized the “number 18” factoid was already posted.
the distance is the same, back & forth
True, but that doesn’t answer the original question.
I can only try-
My sister once showed me some math mix ups that actually work. For example:
19/95 => cross out the 9 from the numerator and denominator => 1/5.
Can you think of any others? (I don’t know of any off hand.)
I was once sitting next to someone on the train who was doing his homework and he was solving for x.
He had 2x = 24. So he crossed out the 2 from both sides and circled x = 4. I was in so much pain so I asked him if I could help, I told him I liked math in school.
“Sir”, he replied, “this isn’t regular math, it’s college level algebra, it’s not as easy as it looks. I don’t think you’ll be able to help me.”
Dr. Pepper, I was wondering what that old old software program is.
Dr. Pepper-
Can you think of any others?
Probably not.
…it’s college level algebra, it’s not as easy as it looks…
My, oh my.
I’m not sure if my response should be “LOL” or “I despair of today’s youth”.
Wow.
Dr P & ICot among others
It’s great to see people who love math!
Here are some interesting mathematical properties, but not necessarily “mixups”:
16- is the only integer where m to the nth power = n to the mth power (2 to the 4th power or 4 to the 2nd power)
17 -is the first number that can be written as the sum of a positive cube and a positive square in two different ways; that is, the smallest n such that x3 + y2 = n has two different solutions for x and y positive integers. The next such number is 65.(2cubed plus 3squared (8+9) or 1cubed plus 4squared (1+16))
23- The sum of the first 23 primes is 874, which is divisible by 23!
24- the product of any 4 consecutive numbers must be divisible by 24
25- is a perfect square (5*5) & is the sum of 2 perfect squares: 3squared(3×3=9) + 4squared(4×4=16)
36- is a square triangular number, i.e., it can be represented as both a square & triangle using x’s (or o’s)
(I tried the triangle above..try it yourself, you should get it!)
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x
.
x
x x
x x x
x x x x
x x x x x
x x x x x x
x x x x x x x
x x x x x x x x
36- multiplied by any other number always produces a quotient whose individual digits add up to nine:
36 x 2 = 72 (7 + 2 = 9)
36 x 36 = 1296 (1 + 2 + 9 + 6 = 18) (1 + 8 = 9)
36 – is the smallest integer which can be expressed as the sum of consecutive primes in 2 ways:
36= 5 + 7 + 11 + 13
and
36= 17 + 19
37 -is the only two digit number (in base 10) that when you multiply by 2 and subtract 1, results in the original number backwards!!!
37- is the only two digit number (in base 10) with the following property:
The difference between the two digits (absolute value) equals the square root of the difference between the original number and the least common multiple of the two digits.
7-3=4
4squared = 16
7 x 3 = 21 (least common multiple)
37 – 21 = 16
square root of 16 = 4!
37- very interesting mathematical properties of 37:
111: 1+1+1=3 and 3 x 37 = 111
222: 2+2+2=6 and 6 x 37 = 222
333: 3+3+3=9 and 9 x 37 = 333
…
999: 9+9+9=27 and 27 x 37 = 999
44- is a happy number (replace 44 by the sum of the squares of its digits, and repeat the process until it equals 1)
4squared + 4squared = 16+16=32
3squared + 2squared = 9+4=13
1squared + 3squared = 1+9=10
1squared + 0squared = 1+0=1
44- the number of derangements of 5 items (44 permutations where none of the elements appear in their original position)
***TRY IT! IT’S FUN!***
HINT:
9 is the number of derangements of 4 items ABC&D:
BADC, BCDA, BDAC,
CADB, CDAB, CDBA,
DABC, DCAB, DCBA
(all other permutations result in at least one in the original position)
45- the sum of the digits 987654321 is 45.
the sum of the digits 123456789 is 45.
The difference between these 2 numbers is 864197532…
GUESS WHAT!
This difference also adds up to 45!!!
48- is a semi-perfect number (equals the sum of some/all of its divisors)
Its 10 divisors are 1,2,3,4,6,8,12,16,24,&48 (1×48, 2×24, 3×16, 4×12, & 6×8)
48= 2+4+6+12+24
49- is the first square (7×7) where the digits (4&9) are also squares
49- the sum of the digits of 49squared (2401: 2+4+0+1=7) is the square root of 49 (7×7=49)! AMAZING!
splenda–
Correct!
This will be the correct answer, regardless of the length of the trip.
And now for the bonus round:
Can anyone express the calculation as a formula?
am yisrael chai–
It’s great to see people who love math!
The factoids you give are very interesting.
One point about the following one:
36- multiplied by any other number always produces a quotient whose individual digits add up to nine:
ICOT,
Total travel time must be a factor. Let’s say the total trip time is 1 hour and 7.5 minutes (1 and 1/8 hours), then the same trip took an extra 7.5 minutes – is it possible that the speed was the same? Obviously not. The amount of time spent driving in one direction hasn’t changed (it was still 60 mph), but the amount of time spent driving back is 7.5 minutes longer. The distance was the same so therefore, the speed must have been lower.
You must have originally come to the same 36 MPH conclusion as I by using a 1 hour travel time when running your numbers. In the latter example (a total trip time of 1 hour and 7.5 minutes), the speed on the return trip will be 30 MPH.
As far as the formula is concerned, I’d be remiss if I failed to point out that a similar riddle was submitted a couple of years ago ==> over here <==, and I used the same formula as was to solve that example.
splenda-
In your example, the trip is 1 hour, 7.5 minutes, i.e. 67.5 minutes.
The average speed for the round trip is 45 MPH, with half the distance traveled at 60 MPH, half at an unknown MPH and an average MPH of 45.
Traveling 67.5 minutes at an average speed of 45 MPH means the total distance traveled is 50.625 miles.
Half of that distance was at 60 MPH, exactly a mile a minute.
This leaves the other half (25.3125 miles) traveled in 42.1875 minutes (the remaining time).
25.3125 (distance) divided by 42.1875 (minutes) multiplied by 60 gives a MPH of 36.
(btw, nice to have you back here)
Yup. I took these from dz’s sfiras haomer game & we were up to day # 36, the day I came back 🙂
“18 is the only number whose digits sum to half its value.”
0, too 😉
One word answers the following:
1. The word has seven letters (ok, that’s a BIG clue)….
2. Preceded G-d… (not apikorsus, have no fear)
3. Greater than G-d…(same as above)
4. Worse than ???…
5. Poor people have a lot of it…
6. Wealthy people may need a lot of it….
7. If you eat it, you will die ch”v.
What is it?
Icot, it’s been a long time since you posted an original…
Does anyone have a riddle to share?
Q) Why were the little strawberries upset?
A) Because their parents were in a jam.
Q) How do crazy people go through the forest?
A) They take the psycho path.
Old joke, those of you that dont know it i suggest you …—- The mods won’t approve what I’m about to say so I’d better keep the mods from one less thing for them to do!! Afterall I’m a kind guy! What’s black and white and red all over???
A news paper!
Mpc
I see you like the b&w & red all over jokes, so try this:
http://www.theyeshivaworld.com/coffeeroom/topic/black-white-and-read-all-over
am yisrael chai-
The answer to One word answers the following: is “Nothing.”
I saw that one several years ago and didn’t want to chapp it, but no one else answered it.
Icot, it’s been a long time since you posted an original…
Sorry – this is the thread I enjoy most, but I’ve been busy lately. B’n I’ll post something reasonably soon.
Let us count the ways
You are presented with two full glasses of water.
One glass contains 100% pure fresh water.
The other glass is saltwater, containing as much salt as can be dissolved.
How many different methods of determining which glass is which can you think of?
see how well it floats objects
measure the specific gravity with a urine dipstick
put a goldfish in both, see which survives
see whick conducts electricity better
weigh both on an extremely accurate scale (im not sure about this one)
heat it up or let it evaporate and see if there is a residue of crystallized salt
put a cathode and anode in it and see if chlorine gas is released
put salt in both and see which one precipitates out first
thats enough im busy
measure the viscosity
put a little more liquid in and gauge the meniscus
cool both, the salt will come out of solution, that might be the same as a prior answer i gave.
measure the osmolarity
have someone else taste it and report their findings
Cut your finger and pour some water from each glass on the wound.
Put some in your etes.
take 2 portions of unsalted meat
pour one glass on each piece
rinse it off
take both pieces to the Godol Ha Dor and ask which is kosher
Let us count the ways – (some) Answers
– see how well it floats objects (Moderator-80)
– measure the specific gravity with a urine dipstick (Moderator-80)
– put a goldfish in both, see which survives (Moderator-80) [along those lines, water a plant with it, or see which one a pet will drink]
– see which conducts electricity better (Moderator-80)
– heat it up or let it evaporate and see if there is a residue of crystallized salt (Moderator-80)
– put a cathode and anode in it and see if chlorine gas is released (Moderator-80) [interesting]
– put salt in both and see which one precipitates out first (Moderator-80) [yep, the one that has already dissolved the max amount wont dissolve any more]
– put a little more liquid in and gauge the meniscus (Moderator-80)
– cool both, the salt will come out of solution, that might be the same as a prior answer I gave. (Moderator-80)
– measure the osmolarity (Moderator-80) [say what??? ]
– have someone else taste it and report their findings (Moderator-80)
– Cut your finger and pour some water from each glass on the wound. (ronrsr)
– Put some in your eyes. (ronrsr) [ I never swam in the ocean. Does it sting?]
– take 2 portions of unsalted meat
pour one glass on each piece
rinse it off
take both pieces to the Godol Ha Dor and ask which is kosher (Moderator-80)
Also, saltwater freezes at a lower temperature and boils at a higher temperature than fresh water.
Put some in your eyes. (ronrsr) [ I never swam in the ocean. Does it sting?]
depends on how salty it is. If it’s about the salinity of tears, it won’t hurt. If it’s much saltier, it will. Try swimming in the Dead Sea; it hurts.
Tongue Twisters
If you must cross a coarse cross cow across a crowded cow crossing, cross the coarse cross cow across the crowded cow crossing carefully.
Does this shop stock short socks with spots?
The sixth sheik’s sixth sheep’s sick. (according to “The Guinness Book of World Records” this is the toughest tongue twister. I’m not great at tongue-twisters, but for some reason, I never had a hard time with it.)
The bun is better buttered,” Betty muttered.
Seven sleek sleepless sleepers seek sleep.
Sixty-six sickly chicks.
The sun shines on shop signs.
The shady shoe shop shows sharp sharkskin shoes.
The bootblack brought the blank book back.
A noise annoys an oyster, but a noisy noise annoys an oyster more.
Rush the washing, Russel!
The seething sea ceaseth seething.
Awful old Ollie oils oily autos.
Mummies munch much mush.
This is a zither.
Ike ships ice chips in ice chip ships.
She says she shall sew a sheet.
Feed the flies fly food, Floyd!
Miss Smith dismisseth us.
Ted threw Fred thirty-three free throws.
Rex wrecks wet rocks.
Can anyone contribute to the cause here??!
Fix the Prefix
(from a calendar)
Use the same three letter word to complete the four words below:
– – – FOLD
– – – URE
– – – ABLE
– – – NIS
Ten
do another one plz 😉
(from a puzzle magazine)
Noach , Chaim and Zundel are drivers for the transit authority.
Each drives a separate route in Brooklyn; one on 60th St., one on 50th and one on 39th.
They started their routes at the same time, from First Avenue towards the higher numbered avenues.
1) The 60th St. bus reached Sixth Avenue last.
2) The B bus, driven by Noach, was crowded.
4) The B bus went up 50th St.
5) The bus going up 39th St. arrived at Sixth Avenue before the others.
6) Who drove each bus, what route did each drive, and in which order did they reach Sixth Avenue?
A Nugget of Wisdom
(also from a puzzle magazine)
“Delightfully Kosher”, a restaurant, sells three different serving sizes of chicken nuggets; 6 pieces, 9 pieces or 20 pieces.
If you want 12 pieces, you can simply order two six-piece servings.
If you want 13 pieces, you are unable to buy exactly what you want.
What is the largest number of pieces that you are unable to order exactly, based on the serving sizes available?
Oh, and congrats to “am yisrael chai” for getting the correct word in “Fix the Prefix”.
Icot
Thanks so much for posting new riddles and for the congrats.
I’m not able yet to do riddles on this WTC yahrtzeit, but perhaps another time. Thanks for the chizuk on the other thread.
New riddle: What travels 60 nanoseconds faster than the speed of light (measured over a distance of 500 miles)?
Hint: it starts with an “h” and ends with an “oax”.
Bus: A B C
Driver: Chaim Noach Zundel
Route: 60th St. 50th St. 39th St.
Place: 3rd 2nd 1st.
A Nugget of Wisdom – Answer
44 = 6+6+6+6+20
45 = 9+9+9+9+9
46 = 6+20+20
47 = 9+9+9+20
48 = 6+6+9+9+9+9
49 = 9+20+20
Once we managed six consecutive numbers, any higher number can be achieved simply by adding a multiple of six to the above numbers.
Using the letters once, rearrange them into a 3×3 grid to spell 6 words – 3 words across and 3 down:
A E E E H O R S T
H O T
A R E
S E E
When the day after tomorrow is yesterday, today will be as far for Shabbos as today is from last Friday if today were yesterday. What day of the week is today?
What is special about today?
Today is 63
Last year was 62
Ten years ago was 61
Eleven years ago was 60
Yesterday was 59
Ten days ago was 55
A month ago was 47
Need any more clues?
The answer to my riddle above is: Today is Monday.
squeak: I can’t figure it out, Got any more clues?
I guess Dr. Pepper is back in his bunker, but this time was definitely not my fault. I know this was his type of riddle, so too bad.
The answer is, what is special about today is that its the last binary day in our lifetimes.
Now back to MY bunker.
Hey, squeak, no bunker for you! You gotta give the rest of us folk a chance to get on here and figure it out!
Now please do another one.
And tell Icot that he’s run out of vacation days.
SQUEAK?!?!
Job interview riddles:
Asked at Google
Asked at Microsoft
Asked at Google
4. A book has N pages, numbered the usual way, from 1 to N. The total number of digits in the page numbers is 1,095. How many pages does the book have?
Asked at Google
5. A man pushed his car to a hotel and lost his fortune. What happened?
Asked at Google
6. You are shrunk to the height of a nickel and thrown into a blender. Your mass is reduced so that your density is the same as usual. The blades start moving in 60 seconds. What do you do?
Asked at Google
#5) playing monopoly
hey blinky
good to see you around
stamamen-
1) ?
2) The balloon will move forward. Since the denser air will move back, it will move the less dense helium balloon forward.
3)
a) Turn both hourglasses over.
b) When the four-minute glass is emptied (4 minutes elapsed, three minutes left in the 7-minute timer) turn it over.
c) When the seven-minute timer is emptied (seven minutes elapsed, one minute left in the four minute timer), turn the seven minute timer over.
d) When the four minute timer is emptied (eight minutes elapsed, six minutes left on the seven minute timer), turn the seven minute timer over, and one minute’s worth of sand will now run out.
4) 9 pages with 1 digit for a total of nine. 90 pages with two digits for a total of 180. 1095 – 189 = 906. 906 / 3 = 302. 302 + 90 + 9 = 401.
5) answered by “blinky”
6)
a) If there is no liquid in the blender: Is there enough clearance to lie down below the blades? Is there clearance to stand between the blade tips and the blender wall?
b) If there is liquid in the blender: Is it high enough that he can climb over the top? Hide in the top? Can he pop the blade off of the base? Can he bend the blades? Can he hold the hub of the blade while it spins? Can he rock the blender so it falls over? Can he say Shema within sixty seconds?
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