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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.
DEAL * DEAL = ----DEAL
Replace dashes by decimal digits,
using reasoning only.
There is only one solution!
<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)
Allow use of concatenation, +, -, x, /, sqrt, exponentation, factorial,decimal fractions, overline & brackets.
Source: Inspired by Martin Gardner statement.
From a set of 2n+1 consecutive integers a certain number, say x, is selected in a way that the remaining n pairs can be arranged as couples having the same sum.
What are all the possible values of x making such task doable?
At a meeting of the Young Historical Society (YHS) in a local library the number of children present
was three times the number of parents.
At this meeting, each boy borrowed 12 books from the
library, each girl borrowed 17 books and each parent borrowed 9 books.
In total 305 books were
How many girls were there at the YHS meeting?
In the equation A*B=C
is an 8-digit number without repeated digits B
is a single digit, not present in A C
is a number containing all non-zero digits.
Sample solution: (A, B, C)= 51249876*3=153749628
Find additional solutions.
The digits of this six digit number N
in some order.
Given that :
DEF/ABC is an integer number
find all possible values of N.
The above 9-digit alphametic is solvable (go for it), but the 10-letter English equivalent (six*five= thirty
) is not!
Why not? Where's the contradiction?
Consider a semi-circle of radius r.
A curve C is drawn such that at any point P on C, the distance between P and the semi circle's base equals the length of a line segment from P perpendicular to the given semi-circumference.
Derive C's equation.
Let's denote by p(n) the greatest square less than or equal to n,
n being a positive integer.
List all pairs (m,n), for which:(2m+1)*p(2n+1) = 400; m being less than n.
A four-digit PIN number aabb
, where a
are distinct digits, is a multiple of 15.
of a are not possible?