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.

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

My foot reversed direction.

SEQUENCE
45

LIARS
Thursday

SQUARE
11X+18

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

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