Alex, Bret, Chris, Derek, Eddie, Fred, Greg, Harold, and John are nine students who live in a three storey building, with three rooms on each floor. A room in the West wing, one in the centre, and one in the East wing. If you look directly at the building, the left side is West and the right side is East. Each student is assigned exactly one room. Can you find where each of their rooms is:
Harold does not live on the bottom floor. Fred lives directly above John and directly next to Bret (who lives in the West wing). Eddie lives in the East wing and one floor higher than Fred. Derek lives directly above Fred. Greg lives directly above Chris.
He originally had a total of 54 gallons of milk in three churns, and he wanted to make sure each churn contained 18 gallons of milk.
In order to do this, he did the following:
First, he poured 1/4 of the first churn into the second churn. He then poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn.
How many gallons did each churn contain before Farmer Stone started pouring?
Hint
Try working backwards, with each churn containing 18 gallons.
Answer
12, 33, and 9 gallons respectively for churns 1, 2, and 3.
Reasoning
Working backwards, at the end after Pour 3, the churns (C1, C2, C3) contained:
C1 C2 C3
————————————
18 18 18 after Pour 3
Pour3 was 1/3 of C3 into C1, the remaining 2/3 has to be the 18 gallons left in C3 after the pour, which means that 1/3 is 9 gallons. So 9 gallons was poured from C3 into C1. Before Pour3, C1 must have contained 9 gallons, and C3 contained 27 gallons.
C1 C2 C3
————————————
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour2 was 1/2 of C2 into C3, the remaining 1/2 has to be the 18 gallons left in C2 after the pour, which means that 1/2 is 18 gallons. So 18 gallons was poured from C2 into C3. Before Pour2, C2 must have contained 36 gallons, and C3 contained 9 gallons.
C1 C2 C3
————————————
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour1 was 1/4 of C1 into C2, the remaining 3/4 has to be the 9 gallons left in C1 after the pour, which means that 1/4 is 3 gallons. So 3 gallons was poured from C1 into C2. Before Pour2, C1 must have contained 12 gallons, and C2 contained 33 gallons.
C1 C2 C3
————————————
12 33 9 at the start
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
During a recent gymnastics gala, four athletes competed in three events, the vault, the beam, and the floor.
Chris came third on the floor. The athlete who came second in the vault won the beam event. The athlete who came second on the beam won the floor. Emery beat Alex in every event. The athlete who won the vault came second on the floor. Billie came last in the vault.
Can you determine who finished where in each event?
Hint
Could Alex have come first or second in any event?
Answer Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Emery Chris
#4 Billie Alex Alex
Reasoning
By (1), Chris came third on the floor. By (6), Billie came last in the vault.
Vault Beam Floor
#1
#2
#3 Chris
#4 Billie
By (2), the athlete who came second in the vault won the beam event, let's mark these as X.
By (3), the athlete who came second on the beam won the floor, let's mark these as Y.
By (5), the athlete who won the vault came second on the floor, let's mark these as Z. Vault Beam Floor
#1 Z X Y
#2 X Y Z
#3 Chris
#4 Billie
By (4), Emery beat Alex in every event, therefore Alex can't have won any event, nor come second (because of X, Y, and Z). So, Alex came third on the vault, and last on the floor. Vault Beam Floor
#1 Z X Y
#2 X Y Z
#3 Alex Chris
#4 Billie Alex
Looking at the vault, Z can't be Chris because Z came second on the floor (but we know Chris came last). So, Z must be Emery, and X is Chris. Vault Beam Floor
#1 Emery Chris Y
#2 Chris Y Emery
#3 Alex Chris
#4 Billie Alex
Looking at the floor, Y is Billie. Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Chris
#4 Billie Alex
By (4), Emery beat Alex on the beam. Vault Beam Floor
#1 Emery Chris Billie
#2 Chris Billie Emery
#3 Alex Emery Chris
#4 Billie Alex Alex