A jar contains every integer from 0 to 20 inclusive, written on slips of paper.  Three numbers are pulled from the jar randomly.  The largest of the three is the sum of the other two. One of the numbers is one less than twice another.  The sum of the numbers is 34. Then, all the numbers were put back in the jar, and three slips were drawn again. Surprisingly, the same statements made above were still true, even though the same three slips were not drawn. Which number was drawn both times?

A clock has a bell that chimes in each of the following ways:

Once at 15 minutes past the hour
Twice at half past the hour
Three times at 15 minutes before the hour
n times at n o'clock (once at 1:00 AM, twice at 2:00 AM, etc).
If the hour is after noon, the clock chimes 12 extra times on the hour (13 times at 1:00 PM, 14 times at 2:00 PM, etc).

How many times will the clock chime between 10:17 AM and 7:35 PM?

The sum of two numbers is 47, and their difference is 30. What are the two numbers?

My son and I went to orange grove and picked some oranges. On the way home I met my friend Sue and gave her half the oranges. Then my son begged me for an orange, so I gave him one. A few minutes later I met my friend Jose, and gave him a quarter of my remaining oranges. My son then asked for another orange, so I gave him one. Then, a few minutes later, my friend Marcus passed by so I gave him half of the remaining oranges. When my son asked for another orange, I told him he couldn't have it, because the last orange was mine.

How many oranges did my son and I pick?

A school has 100 students. 32 of those students play basketball, and 45 of them play soccer. 24 students play football. There are 21 students who don’t play any sport at all. The number of students who play both basketball and football (but not soccer) is twice the number of students who play all three, and three times the number of students who play both soccer and football (but not basketball). Eight students play both basketball and soccer, but not football. How many students play only soccer?

The temperature rose at a rate of 2 degrees every hour during the day, and at 4:00 in the afternoon it started dropping at a rate of 3 degrees an hour. If the temperature at 8:00 in the evening is 67 degrees, what was the temperature at 8:00 in the morning?

This year Santa was so busy overseeing the business of creating toys that he never got around to managing his lists of good children and bad children.

So he decided to give gifts to the first two out of every three boys, and then a lump of coal to the third.

Similarly, he decided to give a present to the first four out of every five girls, and a lump of coal to the fifth.

Finally, he gave presents to the first three out of every four parents, and coal to the fourth.

The first two families he visited had three boys, two girls, and two parents. The next family he visited had one boy and two girls, and one parent. Then he visited two families which each had one boy, one girl, and two parents, and then he visited a family with five boys, three girls, and one parent.

If he did not give any lumps of coal at the next home, what is the largest possible number of people in that family?