What US State is triply landlocked --( a resident must cross three states to reach an ocean, gulf, or bay)?

Definition: Strictly non-palindromic number or SNP number n is a number not palindromic in any base b with 2 ≤ b ≤ n-2.

Equipped only with the above definition you are asked to perform the following tasks:

1. Show that 47 is a SNP number.

2. Write down the 1st 7 members of an increasing sequence of SNP numbers.

3. Explain the reason for defining b=n-2 as the upper limit.

4. Prove that all SNP numbers above 6 are prime, but not all primes are SNP numbers.

<this word> has one I, two Ls, three Ns, four Es, and five Ss.

Find it and its meaning.

Source: Discovered by Sir Jeremy Morse.

Two concentric circles of radius R and r, with R>r are both intersected by the same secant line. The points of intersection, in order, are A,B,C,D.

Prove AC*CD is constant.

Arrange 4 fours into various expressions to generate all integer numbers, from 1 to 112 inclusive like:

1 = 44 ÷ 44

2=sqrt 4 - (4 - 4) x 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 + 4 × (4 - 4)

... ...

7= 44/4-4

... ...

19=4!-4-4/4

... ...

100=4*4!+sqrt(4*4)

etc

Allow use of concatenation, +, -, x, /, sqrt, exponentation, factorial,decimal fractions, overline & brackets.

Source: Inspired by Martin Gardner statement.