快猫短视频

#206 All square

Set by Colin Beveridge

鈥淲hat ho!鈥� boomed Aunt Nicola. I could tell she was about to talk cricket at me. 鈥淗ave you been following the test match between Pythagorea and Lagrangia?鈥�

鈥淎untie, you know I prefer Navier-Stokes to Ben Stokes.鈥� 鈥淲ell,鈥� she said, 鈥測ou might be interested 鈥� there鈥檚 maths involved! In their first innings, Lagrangia鈥檚 total score was a square number.鈥�

鈥淚nnings?鈥� I asked. 鈥淚t鈥檚 the word for a team鈥檚 turn to bat. They each have two. In their first, the Pythagoreans also got a square number, but they were more than 300 behind!鈥�

鈥淭hat sounds insurmountable.鈥� 鈥淵ou might think so,鈥� she said. 鈥淭hen, when Lagrangia batted again, they added a different square number 鈥� less than 50 鈥� so that their lead and overall total were also square numbers.鈥�

鈥淕oodness.鈥� 鈥淏ut the Pythagoreans battled back in their second innings,鈥� she continued, 鈥渁nd the game ended dramatically in a tie.鈥�

I then knew enough to work out the totals of the four innings in order. What were they?

Solution next week

#205 Buried shields

Solution

The missing section of the broken shield can鈥檛 be silver or gold, as those colours would create a shield that is already pictured, so it must be blue.

There are already three shields with two blue sections, as well as three with two grey sections, so the ninth shield must have two gold sections.

The only combination that isn鈥檛 already pictured is shown above.