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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 46
Many years ago, a cruise liner sank in the middle of the Pacific Ocean.
The survivors luckily landed on a remote desert island.
There was enough food for the 220 people to last three weeks.
Six days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 55 people stranded on the island to now share the original rationed food.
The food obviously had to be rerationed, but everyone was now on onehalf of the original ration, so how many days in total would the food last for, from the day of the original sinking?
Hint: Try a random number of over 50s to see what happens.
Answer: 20,064 fish.
As only 3/4 of the over 50s claimed 16 fish, this averages out to 12 fish each.
Similarly only 1/8 of the under 50s claimed 96 fish, this again averages out to be 12 fish each.
Therefore the total number of fish was 1,672 x 12 = 20,064.
It doesn't matter how many over/under 50s there are.
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