Puzzle 153
Last week, I travelled from Birmingham to Glasgow (via bicycle).
On the first day, I travelled one quarter of the distance.
On day two, I travelled one half of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one third of the remaining distance.
I now have 21 miles left to travel.
How far is it from Birmingham to Glasgow in total?
Puzzle Copyright © Kevin Stone
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Hint
How many miles were left at the start of yesterday?
Answer
336 miles.
Reasoning
To work these numbers out, it is perhaps easier to start at the end and work backwards.
Yesterday I travelled 1/3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 ÷ 2/3) at the start of yesterday.
On day 3 I travelled 3/4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 ÷ 1/4) at the start of day 3.
On day 2 I travelled 1/2 of the distance to leave 126 miles, therefore there were 252 miles (=126 ÷ 1/2) at the start of day 2.
On the first day, I travelled 1/4 of the distance to leave 252 miles, therefore there were 336 miles (=252 ÷ 3/4) at the start of the first day.
Double-Checking
On the first day, I travelled one quarter of the distance (84, leaving 252).
On day two, I travelled one half of the remaining distance (126, leaving 126).
On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5).
Yesterday I travelled one third of the remaining distance (10.5).
I now have 21 miles left to travel.
Puzzle 154
If cat and a half can catch a mouse and a half in a day and a half how many mice can 3 cats catch in 3 days?
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Hint
How many mice does one cat catch?
Answer
Six mice.
1.5 cats catch 1.5 mice in 1.5 days.
so
1 cat catches 1 mouse in 1.5 days.
1 cat catches 2 mice in 3 days.
Therefore
3 cats catch 6 mice in 3 days.
Puzzle 155
- 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: D O G D A Y S.
Puzzle Copyright © Alan Stillson and Frank Longo
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Hint
Column 4 contains a D.
Answer
| D |
A |
C |
S |
| L |
Y |
O |
K |
| A |
T |
E |
D |
| G |
S |
P |
I |
Across: CADS, YOLK, DATE, PIGS
Down : GLAD, STAY, COPE, SKID
Boxes : LADY, SOCK, STAG, PIED
Other anagrams of these words are OK as long as they don't change the answer grid.
Puzzle 156
What letter should complete this sequence:
L A H A R U R E D L {?}
Puzzle Copyright © Kevin Stone
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Hint
These were a famous comedy duo.
Answer
Y.
From Laurel and Hardy, the names have been merged.
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