232. The square of 13 is 169. Take the last digit of the square, 9, and place it in the middle, making 196. This is the square of 14, the next number above 13. What are the next numbers which also have this property?
233. The following multiplication example uses every digit from 0 to 9 at least once. Letters have been substituted for the
digits. Can you replace the letters and make the original multiplication problem?
B O G
x B O G
L Y L E
G G U L
T U O O
U N I T O E
234. There are several ways to come up with 100 by using the digits 0 through 9. One way is: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 100. Another way is 78 3/6 + 21 45/90. Can you come up with 2 more ways?
236. Sheilah is now two-thirds of Sally's age. In six years, Sheilah will be four-fifths of Sally's age. In 15 years, Sheilah will be seven-eighths as old as sister Sally. If they are both under the age of ten, how old are they now?
237. You have a huge box of beautiful decorated tiles, enough to provide a border in two rooms. You really can't figure out how to arrange them, however. If you set a border of two tiles all around, there's one left over; if you set three tiles all around, or four, or five, or six, there's still one tile left over. Finally; you try a block of seven tiles for each corner, and you come out even. What is the smallest number of tiles you could have to get this result?
239. When the two met, one was half the other's age plus seven years. Ten years later, when they married, the bride was thirty, but this time one was nine-tenths the age of the other. How old was the groom? (no fractions, no partial years---whole numbers only.)
240. Mona and Allen went shopping for groceries. They spent half of what they had plus $2.00 at the butcher shop. At the dairy, they spent half of what was left, plus $5.00. At the bakery, they spent half of what was left. The remaining $5.00 was spent on coffee and cake. How much did they start with?