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#222 A question of balance

Set by Howard Williams

Being sentimental, Patty likes to use her grandmother鈥檚 beam scales when weighing out ingredients to make a birthday cake for her own granddaughter. The only problem is that the scales aren鈥檛 accurate as the two arms are of slightly different lengths.

To overcome this, she uses both pans and measures half the required quantity in each. For example, to weigh 2 kilograms of flour, she will put a 1-kilogram weight in the right-hand pan and weigh the flour on the left-hand pan, then place the weight in the left-hand pan and weigh a second batch of flour on the right-hand pan. The combined portions of flour will, she thinks, weigh exactly 2 kilograms.

Is she right or will she have more or less than 2 kilograms?

Solution next week

#221 Logical World Cup

Solution

Four of the rows for wins-draws-losses are easy to fill in:

And/orra 4-0-1

Booleivia 3-1-1

Truenisia 2-2-1

Vennezuela 0-2-3

However, Peruf鈥檚 six points could be 2-0-3 or 1-3-1, and United Gates鈥檚 four could be 1-1-3 or 0-4-1.

So far in the table, there are nine wins and six losses. That means that between them, Peruf and United Gates must have lost three games more than they won. The only combination that permits this is Peruf 2-0-3 and United Gates 1-1-3.