The worlds first riddle!

Mark, yet again, you lead the way.


SIMPLIFY
2-sqrt(3)

KNIGHT
327184

BEELINE
25 miles


1997
After more than 60,000,000 simulations, I get a number that is awfully close to 1/e.
(1996/1997)^1997




A convex polygon contains 20 diagonals.
What is the sum of the measures of the interior angles of the polygon


What is the radius of a circle in which a chord of length 10 is 5 units from the centre



1. All the Eton men in this College play cricket;
2. None but the Scholars dine at the higher table;
3. None of the cricketers row;
4. My friends in this College all come from Eton;
5. All the scholars are rowing-men.
6.

POLYGON
1080 degrees

CIRCLE
sqrt(50)

My friends in this College don't dine at the higher table.

Mark old friend, I thought we had an understanding that you would refrain from giving the correct answers to the hardest questions before breakfast.

POLYGON
1080 degrees

CIRCLE
sqrt(50)

My friends in this College don't dine at the higher table. Clever.


By how many degrees does the measure of an interior angle of a regular
decagon exceed the measure of an interior angle of a regular pentagon


Tim has 6 different pairs of socks.
What is the probability that two randomly
selected socks will be from a matching pair



1. There is no box of mine here that I dare open;
2. My writing-desk is made of rose-wood;
3. All my boxes are painted, except what are here;
4. There is no box of mine that I dare not open, unless it is full of live scorpions;
5. All my rosewood boxes are unpainted.
6.

News flash from Santa City.

All week it has been very nice weather on the North Pole. The head elf said that every day last week had a temperature of minus 35 degrees Celsius, except on sunday and one other day.

Every day he wrote down 5 numbers with which you can determine on what day it wasn't -35 degrees Celcius.

To find out, you need to make -35 with each set of numbers for each day. You have to use every number once and you need to use addition, subtraction, division, and multiplication once each in each expression. Brackets are not allowed.


Monday. 10, 1, 8, 101, 7
Thuesday. 11, 2, 11, 5, 616
Wednesday. 3, 96, 5, 33, 6
Thursday . 13, 81, 15, 104, 4
Friday. 221, 82, 9, 3, 4
Saturday. 68, 4, 62, 2, 8

Edit: numbers are changed.


Give expressions for every day that has a solution for -35, and
Find out what day the head elf was refering to.



Whim

ANGLES
36

SOCKS
1/11

My writing desk is full of live scorpions.

Whim:

Monday: 10-101+8*7/1
Tuesday: 6*(46+39/3)-389
Wednesday: 5*((33+51)/2-49)
Thursday: (4+11)/9*(26-47)
Friday: (3-(4+9)*221)/82
Saturday: 2-68+4*62/8

Looks like Sunday is the only day it wasn't -35.

Whim, your ?'News flash from Santa City.' Is, in my humble opinion the most challenging puzzle on the forum. I am sure it will be copied and become a classic. Not that I would have been able to answer it.

Mark, I am running out of superlatives to adequately describe your posts.

ANGLES
36

SOCKS
1/11

"My writing desk is full of live scorpions." I am no vet, but contact pest control.

I am confident that these latest puzzles will last until dinner at least.

What is the degree measure of an angle whose
complement is 25 percent of its supplement.


A 26-ft string is attached to the top of a 10-ft flagpole.
When the other end of the string is held taut to the ground,

what is the number of square feet in the area of the largest
circle that can be drawn with the end of the string


On a certain test, the average score for the women in the class is 83,
whereas the average score for the men in the class is 71.
If the average score for all the students in the class
is 80.

What percent of the students are women


A pile of pennies, dimes, and
half-dollars - 100 coins in all - is worth $5.

How many dimes are in the pile

But I intended friday to be the day. Problem is with this that if you think there is no solution, some clever puzzler possibly will find one. I am a strickly pen and paper person.


I will change the other numbers so that no brackets are needed.
Thanks for playing.

ANGLE
60 degrees

FLAGPOLE
576*PI square feet

STUDENTS
75%

COINS
39 dimes

Ok, before I check the answers against ?'math problems for 5-7 year olds' :wink:

Try this:

Sit down and extend your Right leg, and make clockwise circles with your foot.

Now, extend your Right hand and draw the number 6 in the air.

Wait, what is your foot now doing?

Not easy is it? Which just goes to show the Right hand and foot uses the same part of the brain. Or does it?

My foot reversed direction.

ANGLE
60 degrees

FLAGPOLE
576*PI square feet

STUDENTS
75%

COINS
39 dimes


Mark, "My foot reversed direction."

Exactly, but if you start your foot anti clockwise, no problem. Likewise, if you return to the original scenario, but draw your 6 from the ?'join' clockwise to the top (backwards) again, no problem. It would appear the brain has trouble with different directions from the same side of the body.

I raise a glass to your ?'Blue' number answer.



The sum of the second and fifth terms of an arithmetic sequence
is equal to the sixth term of the sequence. If this common value
is 25, what is the tenth term of the sequence


Politician A lies on Mondays, Tuesdays, and Wednesdays
but tells the truth on the other days of the week. Politician B lies on
Thursdays, Fridays, and Saturdays but tells the truth the other days of the week. One day, both of them said, "Yesterday was one of my lying days."
On what day did they say this



A square has a side length of x units.
The square's length is then increased by 2 units and its width is increased by 9 units.

By how many square units does the area of the new rectangle
exceed the area of the square
Please express your answer in terms of x.

SEQUENCE
45

LIARS
Thursday

SQUARE
11X+18

Mark, how do you do it? I mean the questions do not appear to have enough information to allow an answer to be formed! Therefore, may I ask, "Is there an area of mathematics in which one might find you wanting?" Quantum Physics for example. Any clue as to an Achilles heel would be most gratefully received. :wink:


SEQUENCE
45

LIARS
Thursday

SQUARE
11X+18


Penultimate ?'easy' questions.

On a recent math test, the mean score for Mr. Bill's first and second
period classes combined was 74%. The mean score in the first
period class was 70%, and the mean score in the second period was 80%.
There was a total of 50 students in the two classes.

How many students were in first period


Two sides of an isosceles triangle have measures of
x + 10 and x + 40 and the perimeter of the triangle
is 420 units.

What is the sum of the two possible values of x.


The bases of an isosceles trapezoid are 17 cm and 25 cm,
and its base angles are 45 degrees.

What is the trapezoid's altitude

Oh, c'mon now. I'm sure you find these easy too. I've got plenty of weaknesses. High/middle school geometry and algebra (which many of these are) are not among them.

Why not make these the ultimate 'easy' questions?

MATH
30

TRIANGLE
230

TRAPEZOID
4 cm

MATH
30

TRIANGLE
230

TRAPEZOID
4 cm


Mark, modesty becomes you. Perhaps you could assist with this.

An ancient Pharaoh (is there any other kind) wants to build three identical pyramids on a small island, which is only big enough for one.

Therefore, he comes up with a plan to build the first, then ?'stick' the other two on each side of the first.

Should you sail round the island, how many surfaces will you see

Pyramids:

The second two pyramids could not be identical to the first unless the first had a triangular base. In that case, you would see seven faces.

Unless 'stick' allows placing a side against a side.
Are the base and sides regular?

From the shipo you would see 8 sides.

six triangle sides and two square shaped sides.
The top sides you can't see because normally a pyramid is too high.

Whim

I just knew the wording was wrong for this puzzle. I start again, and yes, I have built a model.

a) Three identical pyramids.
b) One footprint.
c) Two built along opposite sides of first.

"Unless 'stick' allows placing a side against a side.
Are the base and sides regular? "

Yes, and yes.


Should you sail round the island, how many surfaces will you see



Talking about pyramids, what about this!

You have a small pyramidal structure (4 sides, 4 points, and 6 edges). Two ants rest at two different points on the pyramid. They simultaneously move to different points on the pyramid, moving along an edge of the pyramid. They arrive at their new points at exactly the same time, and then begin again toward different points. If they can never touch the same edge twice (regardless of which ant touched it - Ant A can't touch the same edge touched by Ant B, for example), and can never meet on any point or edge.

What is the maximum number of different edges the ants can traverse

What is the answer to the preceding problem for three ants

How about for four ants