- BUYING RIBBON
Mary's mother was Mrs. Jones. Now:Daughters.Hilda bought 4 yds. for $ .16
Gladys bought 6 yds. for .36
Nora bought 9 yds. for .81
Mary bought 10 yds. for 1.00Mothers.Mrs. Smith 8 yds. for $ .64
Mrs. Brown 12 yds. for 1.44
Mrs. White 18 yds. for 3.24
Mrs. Jones 20 yds. for 4.00- SQUARE AND TRIANGULARS
Answers 271To find numbers that are both square and triangular, one has to solve the
Pellian equation, 8 times a square plus 1 equals another square. The succes-
sive numbers for the first square are 1,6, 35, etc., and for the relative second
squares 3, 17, 99, etc. Our answer is therefore 1,225 (35^2 ), which is both a
square and a triangular number.
- PERFECT SQUARES
Several answers can, of course, be found for this problem, but we think the
smallest numbers that satisfy the conditions are:
a = 10,430, b = 3,970, c = 2,114, d = 386.
a + b = 10,430 + 3,970 = 14,400 = 1202.
a + c = 10,430 + 2,114 = 12,544 = 1122.
a + d = 10,430 + 386 = 10,816 = 1042.
b + c = 3,970 + 2,114 = 6,084 = 782.
b + d = 3,970 + 386 = 4,356 = 662.
c + d= 2,114 + 386 = 2,500 = 502.
a + b + c + d = 10,430 + 3,970 + 2,114 + 386 = 16,900 = 1302.