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A Leg to Stand On

Stage: 3 Short Challenge Level: Challenge Level:1

206 legs - the 6 legs of the staff = 200 legs

Each table without customers has 19 legs (1 table and 4 chairs)
Each table with customers has 27 legs (1 table, 4 chairs and 4 customers)

There are 3 times as may tables with customers as without.

3 tables with customers and 1 table without customers has 100 legs (3 x 27 + 19)

So we need twice as many tables (6 with customers and 2 without customers).

8 tables require 32 chairs.


206 - the 6 legs of the staff = 200

On average, at each table, there are three table legs, 16 chair legs and 6 customer legs which gives a total of 25 legs per table.

200/25 = 8, hence there are 8 tables and therefore 32 chairs.

This problem is taken from the UKMT Mathematical Challenges.