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
V
O
L
S
I
B
O
A
E
L
Note: this puzzle is not interactive, and the squares cannot be clicked.
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.
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Puzzle 58
My first is in camel, and in hamster.
My second is in otter, but not in ferret.
My third is in mustang, but not in horse.
My fourth is in snake, and in asp.
My last is in tiger, and in panther.
Reasoning
My first is in camel, and in hamster = AEM
My second is in otter, but not in ferret = O
My third is in mustang, but not in horse = AGMNTU
My fourth is in snake, and in asp = AS
My last is in tiger, and in panther = ERT
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Puzzle 59
Tommy: "How old are you, mamma?"
Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."
Tommy: "That's a lot, isn't it? And how old are you, papa?"
Papa: "Just six times as old as you, my son."
Tommy: "Shall I ever be half as old as you, papa?"
Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."
Tommy: "And supposing I was born before you, papa; and supposing mamma had forgot all about it, and hadn't been at home when I came; and supposing--"
Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."
Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of mamma?
Mamma's Age, Amusements In Mathematics, Henry Ernest Dudeney.
Hint
The answer isn't a whole number of years, and algebra might be required.
Answer
29 years 2 months.
Reasoning #1
This answer is taken directly from the original book.
The age of Mamma must have been 29 years 2 months; that of Papa, 35 years; and that of the child, Tommy, 5 years 10 months. Added together, these make seventy years. The father is six times the age of the son, and, after 23 years 4 months have elapsed, their united ages will amount to 140 years, and Tommy will be just half the age of his father.
Reasoning #2
Here's my answer, with a little algebra.
If we call Tommy T, Mamma M and Papa P we can see that:
"our three ages add up to exactly seventy years" gives us:
(1) T + M + P = 70
"Just six times as old as you" gives us:
(2) P = 6 x T
In an unknown number of years (Y) "Shall I ever be half as old as you" gives us:
(3) P + Y = 2 x (T + Y)
and "our three ages will add up to exactly twice as much as today" gives us:
(T + Y) + (M + Y) + (P + Y) = 140
which can be written as
(4) T + M + P + 3Y = 140
We can see from (4) and (1) that
3Y = 70
so
(5) Y = 70 ÷ 3
Using (2) and (5) in (3) we have
P + Y = 2 x (T + Y)
6 x T + 70 ÷ 3 = 2 x (T + 70 ÷ 3)
4 x T = 70 ÷ 3
(6) T = 70 ÷ 12
We can now use (6) in (2) to see that:
P = 6 x T
P = 6 x 70 ÷ 12
P = 70 ÷ 2
And using the values for T and P in (1) we have:
T + M + P = 70
70 ÷ 12 + M + 70 ÷ 2 = 70
Multiply throughout by 12 to give:
70 + 12 x M + 420 = 840
12 x M = 840 – 420 – 70
12 x M = 350
M = 350 ÷ 12
So:
Tommy = 70 ÷ 12 = 5.83333 = 5 years 10 months. Papa = 70 ÷ 2 = 35 = 35 years. Mamma = 350 ÷ 12 = 29.1666 = 29 years 2 months.
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Puzzle 60
Alex and Billie have to empty all of the bookshelves in the library, and move the books into storage.
Alex, on her own, can empty the bookshelves in 18 hours.
Billie, on her own, can also empty the bookshelves in 18 hours.
Unfortunately, Drew likes to move the books from storage back onto the bookshelves, and she can refill the bookshelves in 36 hours.
How long will it take the three of them, working at the same time, to empty the bookshelves?
Reasoning
In 36 hours, Alex could empty 2 lots of bookshelves, Billie could also empty 2 lots of bookshelves, and Drew could refill 1 lot of bookshelves.
So, 2 + 2 – 1 = 3 lots of bookshelves in 36 hours. Which is 12 hours for one lot of bookshelves.
Alternative Reasoning
Alex and Billie can each empty 1/18 of the bookshelves in 1 hour, but Drew will refill 1/36 of the bookshelves in one hour.
So in one hour we have 1/18 + 1/18 – 1/36 = 1/12.
So it would take 12 hours to empty the bookshelves.
