231. What would be the next number in the following sequence?

11
1,331
161,051
19,487,171 __ ?__

2,357,947,691. The numbers are 11 to the first power, 11 to the third power, 11 to the fifth power, 11 to the seventh power; so the missing number is 11 to the ninth power.

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?

157 squared is 24649, and 158 squared is 24964.

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

8 4 3

x
8 4 3

__ __

2 5 2 9

3 3 7 2

6 7 4 4

__ __

7 1 0 6 4 9.

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?

There are several ways, but here are two:

97 30/45 + 2 6/18; 89 + 6 1/2 + 4 35/70.

235. If 1/2 of 16 were 13, what would 1/3 of 32 be?

17 1/3. If you set it up as a proportion it's easier to see:

__1/2 (16) __
= __1/3 (32)__

13
x

Cross multiplying gives:

8x = 416/3

x = 416/24

x = 17 1/3.

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?

Sheilah is 6, and Sally is 9.

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?

There are 301 tiles. This is the smallest number that will give you a remainder of 1 when divided by 2, 3, 4, 5, and 6, but divided by 7 leaves no remainder.

238. A car company sold 150 cars in a special 6-day tent sale offer. Each day the company sold 6 more cars
than the day before. How many cars were sold on the 6th day?

40. On the first day, the company sold x cars. On the second day, x + 6, on the third day, x + 12, on the fourth day, x + 18, on the fifth day, x + 24,
and on the sixth day, x + 30. If you add all the days together you get the equation:

x + (x + 6) + (x + 12) + (x + 18) + (x + 24) + (x + 30) = 150 cars sold

6x + 90 = 150 and so x = 10.
Therefore, on day 6 (x + 30) = 40.

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.)

The bride was 30; the groom was 27.

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?

$64.00. (first store $32.00 + $2.00, leaving $30.00. Second store $15.00 + $5.00, leaving $10.00; then half is $5.00 and $5.00 remaining).