Plep's Puzzles

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Saturday, August 25, 2007

Lunars

H.G. Wells's novel 'The First Men in the Moon' features intelligent insect-like beings who live in caverns below the surface.
Let us assume that these creatures have a unit of distance called a 'lunar'. It was adopted because the Moon's surface area, expressed in square lunars, exactly equals the Moon's volume, expressed in cubic lunars.
The Moon's diameter is 2160 miles.
How many miles long is one lunar?
(For the purposes of this puzzle, you may assume that the Moon is a perfect sphere).

Saturday, August 18, 2007

Express 100 with five 1's.

Express 100 at least three ways with five 5's.

(I've found seven ways of doing this so far - I'm sure there are more).

Saturday, August 11, 2007

Four 4's - next part

Using arithmetic operations, express the integers from 31 to 50.
You are allowed the standard arithmetic operations, including +, -, *, /, and square root (e.g. sqrt(4)).
The following operations may be useful :
Concatenation. 44 is valid as part of an answer.
Decimals. 4.4 is valid as part of an answer; so is .4 .
Recurring decimals. E.g. .4r (or .4recurring) is the same as .444... - or 4/9 - and valid.
Factorials. The factorial of a positive integer (written as n!) is the product of all the positive integers less than or equal to that number. E.g. 4! = 4*3*2*1 = 24.
Double factorials. The double factorial of an even positive integer (written as n!!) is the product of all the positive even integers less than or equal to that number. The double factorial of an odd positive integer is the product of all the positive odd integers less than or equal to that number. E.g. 4!! = 4 * 2 = 8, and 5!! = 5 * 3 * 1 = 15.
Powers. 4^4 means 4 to the power of 4, and 4^sqrt(4) means 4 squared (or 16). You don't actually need these for these numbers, but you can use them if you like.
Don't use operations like cube roots and inverses (e.g. 1/4). The reason for this is that in normal notation, these use numbers other than 4.

The following may also be useful :
n = sqrt(n) * sqrt(n), n being any number
0 = n-n
1 = n/n (unless n is 0)
2 = (n+n)/n
3 = (n+n+n)/n
10 = 4/.4
5 = sqrt(4)/.4
9 = 4/.4r
3 = sqrt(4/.4r)

Sunday, August 05, 2007

Take the sequence of numbers 123456789.
Place + and - symbols between the numbers so that you get a sum of 100.