A fleet of kids on scooters (2 wheels) and tricycles went whizzing by Igor’s workshop. He was quick enough to count 7 kids and 19 wheels. How many tricycles were there?
Set 09
Bread on Hike
On a hike, twelve high school basketball players carried ten loaves of bread. Each varsity player carried one loaf; each junior varsity player carried a half loaf; and each first-year player carried a quarter loaf. How many players from each team were there, assuming that there was at least one player from each team?
Dripping Faucet
The faucet in my bathroom sink drips one drop every two seconds. If it takes 575 drops of water to fill a 100-ml bottle, how many liters of water are being wasted in a week? A month? A year?
Negative Number Products
Which of the following is not true if h, m, and k are integers and
h < m < k < 0?
- mk < hk
- mh < km
- h + k < m + k
- 0 < k – h
Spirit Week Bake Sale Booth
During Spirit Week, the band decided to have a bake sale every day of the 7-day week. Three booth workers were appointed: a sophomore, a junior, and a senior. Here are the clues about who worked when:
- On only one day of the week were all three students to help.
- No student helped three days in a row.
- No two students were off on the same day more than one time.
- The sophomore was off on Sunday, Tuesday, & Thursday.
- The junior was off on Thursday & Saturday.
- The senior was off on Saturday.
On which day of the week were all three students working?
Cheerleaders’ Three Hats
Three highly intelligent sophomore women, whose names begin with A, B, and C, are trying out to be cheerleaders. They sit in a triangular arrangement to try a puzzle. Each is wearing either a red or gold hat put on her head by the head cheerleader. Each woman can see the other two women’s hats but not her own. The head cheerleader tells them that at least one of the hats is red. Each woman is to look at the other two hats and say nothing, unless she can deduce what color her own hat is. Well, C has been sitting there with her eyes closed the whole time. She never even looks at the other women’s hats. After a few moments of silence, she announces that her own hat must be red. How did she figure it out?
Horse Race (Bedouin)
One sunny day an Englishman was sitting on a rock in the middle of a desert in the domain of Sultan Ibn-al-Kuz. He was bored, since there was absolutely nothing to do, even though he had enough money in his pocket to pay for any kind of entertainment. Thus when he saw two Bedouins riding by, he signaled them to approach.
“Friends,” he said, holding out a shining golden guinea, “I would like you to race to that palm tree over there in the distance, and I will give this golden coin to the one of you whose horse comes in last.”
“Whose horse comes in last?!” exclaimed the Bedouins, who both knew English.
“Exactly so. I realize that this is an unusual condition, but that is what I said. Now start.”
Desirous of money, the two Bedouins started toward the distant palm, but since each of them was trying to hold his horse back, they made very little progress. When they were almost ready to give up the race, a dervish appeared unexpectedly in front of them, and jumping off their horses, they prostrated themselves before him in the hot desert sand.
“What is the trouble, my sons?” asked the dervish in a low voice, and they explained to him the conditions of the race.
“AAh, you are in a tricky situation,” said the dervish. “But here’s what you can do.” And he whispered his advice to them.
“Bless you!” exclaimed the Bedouins, jumping into their saddles and putting their spurs to the horses’ sides.
They galloped to the palm faster than the wind. The race was decided in a few minutes and the Englishman had to pay a guinea to the winner, the one whose horse came in last. What did the dervish say?
Grocer’s Scales (Martha)
Martha the grocer has a 2-pan scale and a set of 4 brass weights. She claims that she can weigh out any whole number of ounces up to 40 ounces using just these weights, and she’s right. What is the weight of each brass weight? (Note that you can put weights on either pan of the scale, so both adding and subtracting are possible.)
Cube View 2
Which of the four cubes on the right could be another view of the cube on the left? No cube has two identical sides unless they’re shown that way in the cube on the left.
Cube Pattern
On the right are four views of the same cube. On the left is the net for the cube. Put the designs on the net where they go. The circles have been placed for you.
