CSC165H1 Study Guide - Final Guide: Well-Ordering Principle, Hit106.9 Newcastle, Natural Number
3
CSC165H1 Full Course Notes
Verified Note
3 documents
Document Summary
There are 800,000 pine trees in a forest. Each pine tree has no more than 600,000 needles. Show that at least two trees have the same number of needles. Show that among any n + 1 numbers one can nd 2 numbers so that their diiference is divisible by n. Show that for any natural number n there is a number composed of digits 5 and 0 only and divisible by n. There are ve points inside an equilateral triangle of side length 2. Show that at least two of the points are within 1 unit distance from each other. Prove that for all a, b z+, exists n z+, such that na > b. Prove that for all n,(cid:80)n k=1 k = n(n+1) Breaking a candy bar with n 1 pieces requires n 1 breaks. For all non-negative x, y, we have that x+y. For any n 1 the following holds:
