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Hint: How many chickens did the last customer buy?
Answer: 15 chickens.
The first customer bought 15 ÷ 2 + ½ = 8 (leaving 7)
The second customer bought 7 ÷ 2 + ½ = 4 (leaving 3)
The first customer bought 3 ÷ 2 + ½ = 2 (leaving 1)
The first customer bought 1 ÷ 2 + ½ = 1
The answer can be worked out in the following way:
The fourth customer can only have bought one chicken, otherwise there would be some chickens left. The third customer bought all but 1, so total - (total ÷ 2 + ½) = 1. This can be solved algebraically or it's easy to see that the total must have been 3. This method keeps working until we reach the first customer.
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 and how many times does the number 3 appear?
Hint: Think of the pages from 1-9, and then 10-99.
Answer: There are 147 pages and the number 3 appears 35 times.
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.
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.
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 re-rationed, but everyone was now on one-half of the original ration, so how many days in total would the food last for, from the day of the original sinking?
Originally there was enough food for 220 people for 21 days, which totals 4620 rations.
After 6 days 1320 rations were eaten.
Therefore there were now 3300 rations for 275 people, which would last for another 24 days at one-half ration per person.
Which is 30 days in total from the original sinking.