The Roman Riddle

Algebra Level 1

Julius "Full-Haired" Caesar is directing a legion of troops (6,000 men) towards Gaul. He has two options:

OPTION 1: Schliffen-Style Manoeuvres

If he goes around the armies of the barbarians, he will be hit by guerrilla attacks that slash 10% of his forces. In the process he will capture undefended towns, and then destroy the barbarians at a battle that will lose him 60% of his remaining forces.

OPTION 2: First Strike

If Caesar does a head-on assault, he will suffer 70% casualties, but not be (literally) decimated by the guerrillas.

Which way conserves more of his forces?

Schliffen-Style Manoeuvres First Strike

2 solutions

Helen Aries
Jul 14, 2017

- If you do it with percenteges, they both start off with 100%

- .the Schliffen-style manouvers looses 10% so:

100%-10%= 90%
of that 60% is then lost: 60% of 90 is 54 therefore 54% is taken away from the 90%
90-54=36
this leaves 36% of the army left

- the first strike looses 70%
100-70=30
this leaves 30% of the army

- Conclusion: 36%>30% therefore the Schliffen-style manouvers loose less men

A Former Brilliant Member
Jul 13, 2017

The answer is that manoeuvres are more effective. This is easily seen: while at first glance they are the same, the 70% total is actually less because the 60% lost in battle is already made less by the 10% loss.

The numerical approach is equally stark: manoeuvring gets us 6000-(6000/10)=6000-600=5400. 5400-(5400/10 6)=5400-3240=2160.* First strike, however, gets us 6000-(6000/10*7)=6000-4200=1800.

Can you please change the options. They seem unclear. You can have options like first way and the second way.

Thank you!

Kaushik Chandra - 3 years, 11 months ago

The Roman Riddle

2 solutions

- If you do it with percenteges, they both start off with 100%

- .the Schliffen-style manouvers looses 10% so:

- the first strike looses 70%

- Conclusion: 36%>30% therefore the Schliffen-style manouvers loose less men

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