Overview
Number
lockers are a kind of crossword puzzle with the clues
leading you to numbers rather than words. In the answers,
you're allowed to use any whole numbers from 1 to 9;
fractions, negative numbers, and 0 aren't allowed.
To
solve number lockers, you don’t need to know anything
beyond the most basic algebra, but you might want to
refresh your memory about the meaning of a few terms.
A square is a number derived by multiplying a
number by itself; for example, 9 is the square of 3 (3
x 3 = 9). If you multiply a number by itself twice, you
get a cube; 27 is the cube of 3
(3 x 3 x 3 = 27). A square (or cube) root is
the number that, when multiplied by itself, yields the
square (or cube); for example, 3 is the square
root of 9, and the cube root of 27. Above cube, we'll
use the term power; 16 is 2 to the fourth power
(2 x 2 x 2 x 2 = 16).
Most
numbers aren’t squares or cubes of any whole number.
16 is a square (of 4). 18 is not (of any whole number).
8 is a cube (of 2), but not a square. 9 is a square (of
3), but not a cube. If a clue asks you for a cube that
fits a single-digit space, you know it must be either
1 or 8 (1 x 1 x 1 = 1; 2 x 2 x 2 = 8). If we ask you
for a cube that fits 2 spaces, the answer could be 27
(3 x 3 x 3) or 64 (4 x 4 x 4). Any other cube would be
too short (the cube or either 1 or 2, either of which
would be a single-digit number) or too long (the cube
of 5 or higher, which would be a triple-or-more-digit
number; for example, 5 x 5 x 5 = 125).
A prime
number can be divided only by itself and 1 without
leaving a reminder. 3 is a prime number; so are 5,
7, 11, 13 etc. 21 is not a prime number because
it can also be divided by 3 and by 7. 1 is not a
prime number.
Consecutive
numbers are numbers that follow one another in
a sequence, like counting consecutively from a lower
to a higher number. (In the rare clues asking for descending
consecutive numbers, the clue or hint will say “descending.”)
Example: “consecutive odd digits” can be
the sequence 1, 3, 5, 7, 9, in that order. (When five boxes
must be filled by that clue, those can be the only possible
answers since you can use only single-digit numbers.)
Smallest or largest
possible number means that the answer cannot have
more or fewer digits than the number of boxes available
for that clue. For example, the smallest possible square
of a prime number that will fit in a two-digit answer
is 25 (5 x 5).
Another
important word to remember is palindrome. A palindrome
(literally “running back” in Greek) is any
phrase, word, or number that reads the same backwards
and forwards. The phrase referring to the Emperor Napoleon’s
exile, “Able was I ere I saw Elba,” is a
palindrome, as is the word “redder.” A palindromic
number might be 33, or 787, etc.
Unities are ones (11 or 111, etc.). So “a cube of unities” that must fit into four boxes must be the cube of 11, which is 1331.
A product of
a number is a result of multiplying that number by any
other number. For example, a product of 15 is 45 (15
x 3); so is 60, and 150.
How
to Begin
As
with crosswords, you can start with easy clues and use
those answers to help you solve more difficult intersecting
ones. If you take a look at the clues in the example
below, you can see that there are many possible answers
for 1 Across, so that wouldn't be a good “entry” for this puzzle.
However,
if you look at 1 Down, “Odd number to the fourth
power,” there’s only one possible answer.
A moment’s trial-an-error calculation will show you that
there are
only two fourth-power numbers with two digits: 16 (2
x 2 x 2 x 2) and 81 (3 x 3 x 3 x 3). Only the second
option could be correct here because the clue states
that you need an odd number.
Once
you get 1 Down, you also know the last digit in 1 Across
(since 1 Across is a palindrome), and you therefore also
know 3 Down.
What
about 2 Down? There are several possible answers, but
only one of them (25) lets you get an answer that fits
the clue to the intersecting 4 Across. Finally, the fact
that 1 Across is a palindrome lets you fill in the final
digit there:
Beware
of Experimenting
with Random Number Combinations
Mistakes
can be costly because elapsed time is key to your score,
If you enter two wrong numbers in any one square, that
square will lock until a correct number is placed in
another square in the grid. You can disable this 2-tries
lockout by checking the box located in the puzzle.
Scoring
A
timing clock starts automatically when you enter your
first number into the game-grid. It runs until you have
entered a number into each of the spaces in the game-grid.
Your score will show the ratio of total correct responses
to total possible responses. It will also show your total
elapsed time.
Select
your own Difficulty Levels
Each number
locker is given a Brain-Gain Level of 1 (easiest),
2 (medium), or 3 (hardest). Click on one of these links
to try games at the level you like. To make any game
more difficult, try not to look at the Help links.
But if you’re having difficulty getting started, HELP
#1 contains clues to the correct words and HELP
#2 gives the correct answer to one of the anagrams.
