Puzzle 129
What four-digit number has …
… Digit 2 smaller than Digit 4 which is two thirds of Digit 1 which is two thirds of Digit 3 which is three times Digit 2?
Puzzle Copyright © Kevin Stone
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Hint
Look at Digit 3 first.
Answer
6394.
Reasoning
Labelling the clues:
Digit 2 is smaller than Digit 4
Digit 4 is two thirds of Digit 1
Digit 1 is two thirds of Digit 3
Digit 3 is three times Digit 2
By (3), Digit 3 is divisible by 3:
Digit 3 = 3, 6, 9
By (3), Digit 1 is two thirds of Digit 3:
Digit 1 = 2, 4, 6.
But, by (2), Digit 1 is divisible by 3:
Digit 1 = 6, and Digit 3 = 9.
By (4), Digit 3 is three times Digit 2:
Digit 2 = 3.
By (2), Digit 4 is two thirds of Digit 1:
Digit 4 = 4.
Puzzle 130
Hidden in the grid below are eight, 7-letter words.
Each word begins with the central R and you can move one letter in any direction to the next letter. All of the other letters are used exactly once each.
What are the words?
| T |
A |
E |
R |
O |
B |
O |
| E |
T |
G |
S |
T |
N |
W |
| R |
N |
E |
E |
A |
I |
E |
| I |
N |
U |
R |
E |
F |
R |
| N |
B |
U |
O |
E |
E |
E |
| B |
S |
E |
A |
E |
V |
E |
| I |
D |
H |
T |
S |
G |
N |
Note: this puzzle is not interactive, and the letters cannot be clicked.
Puzzle Copyright © Kevin Stone
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Hint
One of the words is rubbish.
Answers
Rainbow, referee, revenge, roasted, rubbish, running, retreat, restore.
Puzzle 131
Alex's child, Drew, is exactly one fifth of Alex's age. In 21 years, Alex will be exactly twice Drew's age. How old is Drew now?
Billie is exactly seven times the age of his child, Glen. In 8 years, Billie will be three times the age of Glen. How old is Glen now?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answers
Drew is 7 years old.
Glen is 4 years old.
Answer #1
The first question involves Drew (D) and Alex (A).
Drew is currently one fifth of Alex's age, so:
(1) A = D x 5
In 21 years, Alex will be twice their age, so:
(2) A + 21 = (D + 21) x 2
Using (1) in (2) gives:
A + 21 = (D + 21) x 2
5D + 21 = (D + 21) x 2
5D + 21 = 2D + 42
3D = 21
D = 7
So Drew is 7 (and Alex is 35).
Answer #2
The second question involves Glen (G) and Billie (B).
Billie is exactly seven times the age of Glen:
(3) B = G x 7
In 8 years, Billie will be three times the age of Glen, so:
(4) B + 8 = (G + 8) x 3
Using (3) in (4) gives:
B + 8 = (G + 8) x 3
7G + 8 = (G + 8) x 3
7G + 8 = 3G + 24
4G = 16
G = 4
So Glen is 4 (and Billie is 28).
Puzzle 132
Which four-letter word can be placed between the two following words to make two new words:
arm[----]stand
In the following example, the word 'book' creates the words 'cookbook' and 'bookcase'.
cook[book]case
Puzzle Copyright © Kevin Stone
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Hint
The second letter is A.
Answer
Band.
To give armband, and bandstand.
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