## Pakistan In Control In The Test Match

A look at developments in the test match, some mathematics and plenty of photographs

# INTRODUCTION

The series opener between England and Pakistan is now into its third day of play. This post looks at developments in that match so far.

# THE PAKISTAN INNINGS

A weather hit opening day ended with Pakistan two down, Babar Azam already past 50 and Shan Masood not far short. England bowled well on the second morning but did not get full benefit for their efforts in that department as they were badly let down by Jos Buttler who had an absolute nightmare behind the stumps. Post lunch England bowled poorly, and Masood cashed in, being well supported by Shadab Khan. Masood eventually reached 156 before his resistance was ended. Pakistan tallied 326 in total for their innings, a score that looks very good on this pitch.

# A SOLUTION AND A NEW PROBLEM

I offered this problem from brilliant up in my previous post:

No multi-choice here (this is much too easy for that), but a bonus challenge: part 1) if there was a third square of the same size but divided into 49 smaller squares shaded in similar fashion which would have the largest shaded area, and part 2)what is the general rule relating the number of squares into which the big square is divided and the proportion of it that ends up shaded?

The first shape contains nine squares of which five are shaded, while the second contains 25 squares of which 13 are shaded. 5/9 = 0.55…, while 13/25 = 0.52, so the first shape has a greater shaded area. The 7X7 square would have an even smaller proportion of its area shaded – 25/49 = 0.51. The general rule is that the greater the number of squares the shape is divided into the closer the shaded area approaches to half the total area, while always remaining just above that limit.

Here is another problem from brilliant:

Yasir Shah has just collected his fourth wicket, that of Woakes to make it 170-8, and England are definitely in the mire.

# PHOTOGRAPHS

My usual sign off…