Puzzle 129
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 130
My current age is the age of my favourite book (which is 14 years old) plus one third of my age.
How old will I be when my favourite book is twice its current age?
Puzzle Copyright © Kevin Stone
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Hint
A little algebra might help.
Answer
I will be 35 in 14 years.
Reasoning
I am currently 21.
If X is my current age, then:
X = 14 + X
———
3
so
2X = 14
———
3
and
2X = 42
So
X = 21
I am currently 21 and my favourite book is currently 14 years old, when it is 28 years old (double its age) I will be 35.
Puzzle 131
What number completes this sequence:
4 15 14 11 5 {?}
Puzzle Copyright © Kevin Stone
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Hint
Think of the alphabet.
Answer
25 for Y.
These are the positions of the letters of the alphabet, and they are spelling Donkey.
Puzzle 132
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.
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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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