## August 2016 Logic & Maths Problems

1. How many animals do I have if all but 3 are dogs, all but 3 are cats, all but 3 are pigs and all but 3 are cows?

2. Four people, who are two married couples, each buy one present to throw into a lucky dip. The rules are that no-one may choose the present they brought, or be left with their own present. What is the chance that everyone will get a present that came from their own spouse?
(a) 1 in 9
(b) 1 in 4
(c) 1 in 3

3.
If 180 is the highest possible score a competitor can achieve in a round of darts, what are the next three highest possible scores?

4. What is the total number of rectangles in this figure?

5. Farmer Joe came to town with some watermelons. He sold half of them plus half a melon, and had one melon left over. How many melons did he bring?

6. Lee, Dale and Terry are related to each other.
(a) Among the three are Lee’s legal spouse, Dale’s sibling and Terry’s sister-in-law.
(b) Lee’s legal spouse and Dale’s sibling are of the same sex.
Which one is the married man?

7.
Three sisters are identical triplets. Sarah always tells the truth. Sue always lies. Sally sometimes lies and sometimes tells the truth.

Victor tried to identify them by asking each of them one question.

He asked the sister that was sitting on the left, “Which sister is in the middle?” and the answer he received was, “That’s Sarah.”

He then asked the sister in the middle, “What is your name?” The response was, “I’m Sally.”

Victor then asked the sister on the right, “Who is that in the middle?” The sister then replied, “She is Sue.”

This confused Victor; he had asked the same question three times and received three different answers.

a. Who was on the left?
b. Who was in the middle?
c. Who was on the right?

8. According to the traditional song, on the first day of Christmas (25th December), my true love sent to me a partridge in a pear tree. On the second day of Christmas my true love sent two turtle doves and a partridge in a pear tree. So to this stage, four birds have been accumulated. (Two doves, two partridges).

If the song holds true, and they all survive:

a. how many birds will I have accumulated by the end of the 7th day?
b. how many birds will I receive altogether?

(Reminder: On the 12th and final day you get Twelve drummers drumming, Eleven pipers piping, Ten lords a-leaping, Nine ladies dancing, Eight maids a-milking, Seven swans a-swimming, Six geese a-laying, Five gold rings, Four calling birds, Three French hens, Two turtle doves and a partridge in a pear tree)

9. Four men stand in line. The first in line cannot see any of the three men behind him. The second in line can see the man in front of him but not the men behind him. The third in line can see the first two but not the man behind him. The man at the back can see the other three.

They each wear a hat. “There is a brown hat, a red hat, a blue hat, and a hat that is a duplicate of one of those colors,” they are informed.

Starting with the one in the back, each man was asked in turn what color hat he was wearing. They all gave the correct answer.

Which one of these arrangements would make this possible?

10. A boy and a girl are talking.

“I am a boy” – said the child with black hair.

“I am a girl” – said the child with white hair.

At least one of them lied.

Who is the boy and who is the girl?

SOLUTIONS