MathDB

4

Part of 2016 Online Math Open Problems

Problems(2)

2015-2016 Spring OMO #4

Source:

3/29/2016
Given that xx is a real number, find the minimum value of f(x)=∣x+1∣+3∣x+3∣+6∣x+6∣+10∣x+10∣.f(x)=|x+1|+3|x+3|+6|x+6|+10|x+10|.
Proposed by Yannick Yao
Online Math Open
2016-2017 Fall OMO Problem 4

Source:

11/16/2016
Let G=1010100G=10^{10^{100}} (a.k.a. a googolplex). Then log⁡(log⁡(log⁡10G)G)G\log_{\left(\log_{\left(\log_{10} G\right)} G\right)} G can be expressed in the form mn\frac{m}{n} for relatively prime positive integers mm and nn. Determine the sum of the digits of m+nm+n.
Proposed by Yannick Yao