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• #1069737

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.

#1069738

splenda-

I suspect “Dr. Pepper” knows what the “old old software interface” referenced by “squeak” is.

I do not.

#1069739
am yisrael chai
Participant

d=r*t

distance=rate x time

the distance is the same, back & forth

#1069740

am yisrael chai-

Nice catch!

the distance is the same, back & forth

True, but that doesn’t answer the original question.

#1069741
Dr. Pepper
Participant

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.”

#1069742
splenda
Member

Dr. Pepper, I was wondering what that old old software program is.

#1069743

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.

#1069744
splenda
Member
#1069745
am yisrael chai
Participant

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:

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!

#1069746

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:

#1069747
splenda
Member

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.

#1069748

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)

#1069749
am yisrael chai
Participant

The Sefiras Ha'Omar game!!

The Sefiras Ha'Omar game!!

Yup. I took these from dz’s sfiras haomer game & we were up to day # 36, the day I came back 🙂

#1069750
am yisrael chai
Participant

“18 is the only number whose digits sum to half its value.”

0, too 😉

#1069751
am yisrael chai
Participant

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?

#1069752
am yisrael chai
Participant

Icot, it’s been a long time since you posted an original…

Does anyone have a riddle to share?

#1069753
Tomche
Member

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.

#1069754

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!

#1069755
am yisrael chai
Participant

Mpc

I see you like the b&w & red all over jokes, so try this:

#1069756

am yisrael chai-

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.

#1069757

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?

#1069758

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

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

#1069759

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

#1069760

have someone else taste it and report their findings

#1069761
ronrsr
Member

Cut your finger and pour some water from each glass on the wound.

#1069762

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

#1069763

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.

#1069764
ronrsr
Member

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.

#1069765

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.

#1069766
am yisrael chai
Participant

Can anyone contribute to the cause here??!

#1069767

Fix the Prefix

(from a calendar)

Use the same three letter word to complete the four words below:

– – – FOLD

– – – URE

– – – ABLE

– – – NIS

#1069768
am yisrael chai
Participant

Ten

do another one plz 😉

#1069769

(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?

#1069770

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?

#1069771

Oh, and congrats to “am yisrael chai” for getting the correct word in “Fix the Prefix”.

#1069772
am yisrael chai
Participant

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.

#1069773
squeak
Participant

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”.

#1069774

``````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.

#1069775
am yisrael chai
Participant

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

#1069776
BaalHabooze
Participant

H O T

A R E

S E E

#1069777
BaalHabooze
Participant

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?

#1069778
squeak
Participant

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?

#1069779
BaalHabooze
Participant

The answer to my riddle above is: Today is Monday.

squeak: I can’t figure it out, Got any more clues?

#1069780
squeak
Participant

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.

#1069781
am yisrael chai
Participant

Hey, squeak, no bunker for you! You gotta give the rest of us folk a chance to get on here and figure it out!

And tell Icot that he’s run out of vacation days.

#1069782

SQUEAK?!?!

#1069783
stamamen
Member

Job interview riddles:

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?

5. A man pushed his car to a hotel and lost his fortune. What happened?

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?

#1069784
Participant

#5) playing monopoly

#1069785
Participant

good to see you around

#1069786

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.