70 Arithmetic & Algebraic Problems- THE YEAR 1927
A French correspondent sends the following little curiosity. Can you find
values for p and q so that pq - qP = 1927? To make it perfectly clear, we will
give an example for the year 1844, where p = 3, and q = 7:37 - 73 = 1844.
Can you express 1927 in the same curious way?- BOXES OF CORDITE
Cordite charges (writes W. H. 1.) for 6-inch howitzers were served out from
ammunition dumps in boxes of IS, 18, and 20.
"Why the three different sizes of ,?oxes?" I asked the officer on the dump.
He answered, "So that we can give any battery the number of charges it
needs without breaking a box."
This was ~n excellent system for the delivery of a large number of boxes,
but failed in small cases, like 5, 10,25, and 61. What is the biggest number of
charges that cannot be served out in whole boxes of IS, 18, and 20? It is not
a very large number.
228. THE ORCHARD PROBLEM
A market gardener was planting a new orchard. The young trees were ar-
ranged in rows so as to form a square, and it was found that there were 146
trees unplanted. To enlarge the square by an extra row each way he had to
buy 31 additional trees.
How many trees were there in the orchard when it was finished?
- BLOCKS AND SQUARES
Here is a curious but not easy puzzle whose author is not traced.
Three children each possess a box containing similar cubic blocks, the
same number of blocks in every box. The first girl was able, using all her
blocks, to make a hollow square, as indicated by A. The second girl made