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Hint: Think of the pages from 19, and then 1099.
Answer: There are 147 pages and the number 3 appears 35 times.
Stage 1
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For pages 1  9 we have a total of 9 digits. For pages 10  99 we have a total of 180 digits. This is a total so far of 189, therefore we require another 144 digits, which is another 48 pages. Taking us to 147 pages in total.
Stage 2
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From page 1 to 147 we have 15 times where the page number ends in 3. We also have the ten pages in the 30's, and the ten pages in the 130's that have the extra 3 in them. For a total of 35 number 3s.
Puzzle 84
Each of the 6letter words below can be mixed up and then broken down into two common 3letter words.
HELIUM = HUM + LIE
LATEST = LET + SAT
ALMOND = OLD + MAN
ELDEST = SET + LED
SAFETY = FAT + YES
RADIUM = AIR + MUD
DESERT = RED + SET
WEALTH = THE + LAW
TRICKY = KIT + CRY
FUNNEL = ELF + NUN
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