TO ASCERTAIN A SQUARE NUMBER AT A GLANCE.
Every boy knows that a square number is a number produced by the multiplication of any number into itself; thus 7, multiplied by itself, gives 49 as a result, 49 consequently is a square number, 7 being termed the square root from which it springs. In high numbers the extraction of the square root is an affair of time and trouble, and after all the necessary calculations have been made it may perhaps be found that the number is not a square number. This unnecessary trouble may be saved if the following instructions are remembered:—Every square number ends with one of the figures 1, 4, 5, 6, or 9, or with two ciphers preceded by one or other of those figures. Again, every square number is either equally divisible by 4, or when divided by 4 will have a remainder of 1; thus, as shown above, the square of 7 is 49, which divided by 4 gives us a quotient 12 and 1 over; 64 again is a square number, and it is exactly divisible by 4.
TO DISTINGUISH COINS BY ARITHMETICAL CALCULATION.
Request some person to place in one of his hands a bronze coin and in the other a silver one, and to let no one know which hand contains either particular coin. This may be ascertained by the following calculation:—The calculator should assign an even number, say 4, to the bronze coin, and an odd number, say 7, to the silver coin. The person holding the coins should be requested to multiply the number assigned to the coin held in his right hand by an even number, and that assigned to the coin held in the left hand by an odd number. Instruct that the products of the two calculations be added together, and if the whole sum be even the silver coin will have been placed in the right hand, and the bronze coin in the left. If the result be an odd number, the reverse arrangement will of course have been made.
We will conclude this section by stating shortly some of the
PROPERTIES OF NUMBERS.
By a careful study of these properties many amusing arithmetical puzzles and numerical combinations may be arrived at:—
1. Every odd number multiplied by an odd number produces an odd number.
2. Every odd number multiplied by an even number produces an even number.
3. Every even number multiplied by an odd number produces an even number.