John lists the integers from 1 to 20 in increasing order. He then erases the first half of the integers in the list and rewrites them in order at the end of the second half of the list. Which integer in the new list has exactly 12 integers to its left?
Solution
John first writes the integers from 1 to 20 in increasing order. When he erases the first half of the numbers, he erases the numbers from 1 to 10 and rewrites these at the end of the original list. Therefore, the number 1 has 10 numbers to its left. (These numbers are .) Thus, the number 2 has 11 numbers to its left, and so the number 3 has 12 numbers to its left.
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.