Puzzle 129
I am compiling the new BrainBashers world almanac, and it now contains lots more pages.
I know that it takes 333 digits to print the page numbers in sequence.
How many numbered pages does the book have?
How many times does the number 3 appear?
Puzzle Copyright © Kevin Stone
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Hint
Think of the pages from 1-9, and then 10-99.
Answers
There are 147 pages.
The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.
For pages 10-99, there are 90 pages, which is 180 digits.
This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.
Taking us to 9 + 90 + 48 = 147 pages in total.
Answer #2
From page 1 to 147 we have 15 pages that end in 3:
3, 13, 23, …, 143
We also have the ten pages that start with 30:
30, 31, 32, …, 39
Plus the ten pages that start with 130:
130, 131, 132, …, 139
For a total of 15 + 10 + 10 = 35 number 3's.
Puzzle 130
What comes next in this sequence:
hydrogen helium lithium beryllium boron ?
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Hint
You might need a periodic table.
Answer
Carbon.
From the elements, in increasing order of atomic number.
Puzzle 131
Can you find every occurrence of the word LEMON that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
Puzzle Copyright © Kevin Stone
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Hint
The word LEMON appears 47 times.
Answer
The word LEMON appears 47 times.
Puzzle 132
Starting with WARM, change one letter at a time, and end with COOL?
Each change leaves the other letters in their original places and must result in a proper word.
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Hint
One answer changes Warm to Worm.
Answer
WARM, WORM, WORK, CORK, COOK, COOL
or
WARM, WORM, WORD, WOOD, WOOL, COOL.
