Miscellaneous Puzzles 63- ACCOMMODATING SQUARES
Can you find two three-figure square numbers (no zeros) that, when put
together, will form a six-figure square number? Thus, 324 and 900 (the squares
of 18 and 30) make 324,900, the square of 570, only there it happens there
are two zeros. There is only one answer.
- MAKING SQUARES
Professor Rackbrane asked his young friends the other morning if they
could find three whole numbers in arithmetical progression, the sum of every
two of which shall be a square.
- FIND THE SQUARES
"What number is that," Colonel Crackham asked, "which, added separately
to 100 and 164, will make them both perfect square numbers?"- FORMING SQUARES
"An officer arranged his men in a solid square," said Dora Crackham, "and
had thirty-nine men over. He then started increasing the number of men on
a side by one, but found that fifty new men would be needed to complete the
new square. Can you tell me how many men the officer had?"
- SQUARES AND CUBES
Find two different numbers such that the sum of their squares shall equal
a cube, and the sum of their cubes equal a square.- MILK AND CREAM
Professor Rackbrane, when helping himself to cream at the breakfast table,
put the following question:
"An honest dairyman found that the milk supplied by his cows was 5 per
cent cream and 95 per cent skimmed milk. He wanted to know how much