Answer
There are four boys and six girls in the family.
If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b − 1) = g.
And his sister, Frankie, has one more sister than she has brothers, so g − 1 = b + 1.
2(b − 1) = g [1]
g − 1 = b + 1 [2]
Using [1] in [2] gives:
2(b − 1) − 1 = b + 1
Expanding the bracket gives:
2b − 2 − 1 = b + 1
Simplifying the left hand side gives:
2b − 3 = b + 1
Add 3 to each side gives:
2b = b + 4
Subtract b from both sides gives:
b = 4
Using b = 4 in [1] gives:
2(4 − 1) = g
6 = g
??
Puzzle 2
Farmer Stone is quite an eccentric dairy farmer.
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
??
Puzzle 3
Using all of the letters A to Z, each once only, complete these common words. a-a-e--ave-uie---gonp--otvi-e--ac-t--metb--ep-u-ge-lan--ra-ebon--
During the latest round of the BrainBashers school triathlon the final results were mislaid, however, this is what we do know.
Hayden was fourth. Alex was not the oldest but was older than Drew, who was not second. The child who was next in age to the youngest, finished second. The child who finished in third place was older than the child who finished first. Billie was younger than the child who finished in third place.
Can you determine who finished where and place the children in order of age?
Answer # Name Age
#1 Drew youngest
#2 Billie next to youngest
#3 Alex next to oldest
#4 Hayden oldest
Reasoning
By (2), neither Alex nor Drew were the oldest. By (5), neither was Billie. Therefore, Hayden was the oldest, and by (1) came fourth.
#1
#2
#3
#4 Hayden oldest
By (4) the youngest didn't come third, and by (3) the youngest didn't come second. Therefore, the youngest came first.
#1 youngest
#2
#3
#4 Hayden oldest
By (3), the next to youngest came second, leaving the next to oldest in third.
#1 youngest
#2 next to youngest
#3 next to oldest
#4 Hayden oldest
By (2), Drew wasn't second, but Alex was older, so Drew can't be third either. Therefore, Drew can only have come in first.
#1 Drew youngest
#2 next to youngest
#3 next to oldest
#4 Hayden oldest
By (5) Billie didn't come third, so came second. Leaving Alex in third.
#1 Drew youngest
#2 Billie next to youngest
#3 Alex next to oldest
#4 Hayden oldest
