Puzzle 5
A kind old person decided to give 12 sweets to each of the adults in the town, and 8 sweets to each of the children.
Of the 612 people in the town, exactly half of the adults, and exactly three quarters of the children took the sweets.
How many sweets did the kind old person have to buy?
Puzzle Copyright © Kevin Stone
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Hint
Does the number of adults and children matter?
Answer
3,672.
Reasoning
The actual number of adults and children doesn't actually matter.
If all of the people were adults, then half of them (306) would be given 12 sweets:
306 x 12 = 3672
If all of the people were children, then three quarters of them (459) would be given 8 sweets:
459 x 8 = 3672
If there were 512 adults (so 256 would get 12 sweets = 3072) and 100 children (so 75 would get 8 sweets = 600):
256 x 12 + 75 x 8 = 3672
We can change the numbers of adults and children, but it doesn't change the answer.
The reason for this lies in the fact that 1 /2 adults x 12 sweets = 3 /4 children x 8 sweets (both are 6).
Puzzle 6
Three people check into a hotel.
They pay £30 to the manager and go to their room.
The manager suddenly remembers that the room rate is £25 and gives £5 to the porter to return to the people.
On the way to the room the porter reasons that £5 would be difficult to share among three people so they keep £2 and give £1 to each person.
Now each person paid £10 and got back £1.
So they paid £9 each, totalling £27. The porter has £2, totalling £29.
Where is the missing £1?
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Hint
Be careful of what you're adding.
Answer
We have to be careful what we are adding together.
Originally, they paid £30, they each received back £1, they now have only paid £27.
Of this £27, £25 went to the manager for the room and £2 went to the porter.
Puzzle 7
Place letters into the grid such that every row, column, and 2x2 block has letters (in any order) that form a common word. Each letter is only used once, and no letter is repeated in the rows / cols / blocks.
Letters allowed: W A R M T H
Note: this puzzle is not interactive, and the squares cannot be clicked.
Puzzle Copyright © Alan Stillson and Frank Longo
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Hint
Row 1's missing letter is A which makes Column 4 a little easier to think about.
Answer
V
O
L
A
S
W
I
H
T
B
M
O
A
R
E
L
Across: oval, wish, tomb, real
Down : vast, brow, lime, halo
Boxes : vows, hail, brat, mole
Other anagrams of these words are OK as long as they don't change the answer grid.
Puzzle 8
Which letter is missing from this sequence:
B C E G K Q S W
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Hint
Convert the letters to positions in the alphabet.
Answer
M.
Reasoning
These are letters that occupy prime number positions in the alphabet:
B = 2
C = 3
E = 5
G = 7
K = 11
M = 13 *
Q = 17
S = 19
W = 23
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