Maths Olympiad Exam

Q. 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. Find the integer in the new list which has exactly 12 integers to its left

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Maths Olympiad Other Question

Q. Begin with any two-digit positive integers and multiply the two digit together. If the result product in a two-digit number, then repeat the process. When this process is repeated, all two digit numbers will eventually become a single digit number. Once a product results in a single digit, the process stops.

a) Beginning with number 68, determine the no. of steps required for the process to stop
b)Determine all two digit numbers for which the process stops at 8 after 2 steps.
c) Determine all two digit no. for which the process stops at 4
d) Determine a two digit number for which the process stops after 4 steps
Q. For which positive integral values of m, 1/2m^2+15 will be closest to 0.01