221. Arrange the ten digits 0 to 9 in three arithmetical sums, using three of the four operations of addition, subtraction, multiplication, and division, and
using no signs except the ordinary ones implying those operations. Here is an example to make it quite clear (note that the example is not correct):

3 + 4 = 7 9 - 8 = 1 5 X 6 = 30

7 + 1 = 8 9 - 6 = 3 4 X 5 = 20.

222. Several cartons of candy are being shipped from a manufacturer to warehouses where they will be prepackaged to sell to stores. The candy in each carton
needs to be divided equally among 3, 4, 5, or 7 stores. What is the least number of pieces of candy that each carton can have?

The lowest common denominator for 3, 4, 5, and 7 is 420. 3 x 4 x 5 x 7 = 420.

223. Kevin flew to Puzzleland at the fantastic speed of 1000 miles per hour.
There he picked up his friend and flew back, burdened by the extra weight, at only 500 miles per hour. What was his average speed?

Kevin flew at 666.67 miles per hour over his entire trip.

224. What is the number that is 5 more than the number which is one-fifth of one-fifth of one-half of 1050?

26. (1050 ÷ 5 = 525 ÷ 5 = 105 ÷ 5 = 21 + 5 = 26).

225. The following multiplication example uses every digit from 0 to 9 once (not counting the intermediate steps). Fill in the missing numbers.

7 x x

__
4 x__

x x x x x

226. There are 7 tennis balls which are identical in all aspects except that one of them weighs slightly less than the
other 6. How can you identify the one that weighs less on a balance scale with no more than 2 separate weighings?

Put aside one of the 7 balls and place 3 balls on each pan of the balance scale. If the 2 pans balance out, congratulations, you have already found the
lightest ball (the ball which you have put aside). If the 2 pans do not balance out, clearly the lightest ball is on the pan that goes up. Take the 3 balls that
are on that pan and put the other 3 balls aside.

For the second weighing, take 2 of the 3 suspect balls, putting each one on a separate pan. If the 2 pans balance
out, then the lightest ball is the new one that is put aside. If they do not balance out, then the lightest ball is the one on the pan that goes up.

227. Fill in the missing numbers in the following series:

101 99 102 98 103 97 __?__ __?__

104 96. There are really 2 series in one, one starts at 101 and counts up; the other starts at 99 and counts down 5.

228. Can you arrange the odd digits 1, 3, 5, 7, and 9, and the even digits, 2, 4, 6, and 8, in such a way that the odd ones add up to the same as the even
ones? You can use arithmetical signs and decimals, but the idea is to try and arrive at the simplest possible solution. There are, of course, many
possible answers.

1 + 3 + 7 + 9/5 = 12.8 and 2 + 4 + 6 + .8 = 12.82.

229. Many years ago when gasoline was only 46 cents a gallon, I stopped to fill up my car. I gave the attendant a $20.00 bill and waited for my change.
Unexpectedly, he charged me for the number of gallons that the car needed instead of the dollar amount. (for example if the car took 8.4 gallons he
would have charged me $8.40. Because he did this, I received less in change than I should have. The funny thing is that I had received in
change exactly the amount that I should have been charged for the gas in the first place. Remembering that the cash indicator on a gas pump will only
charge to the nearest half-cent, how many gallons of gas did I buy that day?

13.7 gallons at 46 cents = $6.30 ( to the nearest 1/2 cent.) Therefore, my change from the $20.00 was $6.30 as I had been charged $13.70.

230. What is the four-digit number (no zeros) in which the third digit is the number of "winds," the first digit is one-half of the third, the
second digit is double the third and the last digit is one-half the sum of the first three?