72 Arithmetic & Algebraic Problems- MENTAL ARITHMETIC
To test their capacities in mental arithmetic, Rackbrane asked his pupils the
other morning to do this:
Find two whole numbers (each less than 10) such that the sum of their
squares, added to their product, will make a square.
The answer was soon found.- SHOOTING BLACKBIRDS
Twice four and twenty blackbirds
Were sitting in the rain;
I shot and killed a seventh part,
How many did remain?- THE SIX ZEROS
A B C
III III 100
333 333 000
555 500 005
777 077 007
999 090 999
2,775 I,ll I I, IIIWrite down the little addition sum A, which adds up 2,775. Now substitute
six zeros for six of the figures, so that the total sum shall be I, Ill. It will be
seen that in the case B five zeros have been substituted, and in case C nine
zeros. But the puzzle is to do it with six zeros.
- MULTIPLICATION DATES
In the year 1928 there were four dates which, written in a well-known
manner, the day multiplied by the month will equal the year. These are
28/1/28, 14/2/28, 7/4/28, and 4/7/28. How many times in this century-
1901-2000, inclusive-does this so happen? Or, you can try to find out which
year in the century gives the largest number of dates that comply with the
conditions. There is one year that beats all the others.