We are well familiar with cross-word puzzles. Fun with numbers is also a kind of cross-word puzzle in which we use numbers instead of words. Using numbers, we are free to use any natural number 1 to 9. Negative numbers, fractions and zero (0) are not allowed.
Before we play with numbers, it is necessary to know about some basic terminology of Algebra as follows:
When a number is multiplied by itself, the result is called square of that number e.g., when we multiply 4 by 4, the result is 16. This 16 is called square of 4 and of 4 vise-versa, 4 is called square root of 16. Hence, square root is a number which when multiplied by itself yields the square of that number e.g., 3 when multiplied by 3 itself results in 9 which is square of 3 and 3 is square root of 9.
Similarly, when a number is multiplied two times by itself, we get a cube e.g., 3 × 3 × 3 = 27. Here 27 is cube of 3 and 3 is cube root of 27.
Most of numbers are square but they are not cube e.g., 16, 25, 36, 49 are square but they are not cube. Similarly 8, 27 and 125 are cube of 2, 3 and 5 but they are not square of a natural number. Here by square and cube we mean, generally perfect square and perfect cube.
A prime number is a number which can be divided only by it-self and one without leaving a remainder such as 2, 3, 5, 7, 11, 13, 17 are prime numbers. The smallest prime number is 2. Remember, 1 is not a prime number. 2 is the only even number which is prime.
Consecutive numbers are those numbers which follow one-another in a sequence (order may be ascending or descending) e.g., 1,2,3,4... are consecutive natural numbers.
1, 3, 5, 7, 9...are consecutive odd numbers.
2, 4, 6, 8, 10...are consecutive even numbers.
The smallest or largest possible number meant 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 be fit in two-digit answer is 25, (5 × 5).
The greatest possible cube of a number that will fit in two-digit answer is 64, (4 × 4 × 4).
‘Palindrome’ is an important word to be noted. Palindrome is a number that has same value either from the left side or from the right e.g., 343 is a cube of a prime number which is a palindrome. Similarly, 32523 is also a palindrome since it has same value from either side, left or right.
Another notable from is ‘unities’. Unities is a group of one’s i.e. 11, 111, 1111 etc. are called unities.
‘A cube of unities’ that must fit into four boxes should be the cube of 11 which is 1331.
Multiple of a number means product of that number e.g., 8, 16, 24, 32...are multiples of 8. When 8 is multiplied by 1, 2, 3 and 4., we get 8, 16, 24, 32... One thing more to be noted is 36 is a multiple of 9 as well as that of 4. It is also a multiple of 12 and 18.
Some more important hints which are helpful to understand clues are as follows:
If there is a problem to fit a cube in one block then it must be 1 or 8 i.e. cube of 1 and 2. If there is a problem to fit a cube in two blocks then it must be either 27 (3 × 3 × 3) or 64 (4 × 4 × 4). Other than these two, the cube will be either of one digit e.g. 1 and 8 or more than two digits e.g., 125, 216...etc.
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