#10 Betty鈥檚 change
Betty works at a cash register in the US. When you purchase something from her, Betty always gives you your change the sensible way: by selecting the largest coins that don鈥檛 take her over the amount that she owes you. For example, if she owed you 37 cents, she would first pick out a quarter (25 cents), then a dime (10 cents) then two pennies (a cent each).
However, this morning she has run out of nickels (5 cents) to give out as change, though she has plenty of pennies, dimes and quarters. When she gives you your change, you notice that she has given you twice as many coins as she could have done if she hadn鈥檛 been so keen to always start with the largest coin. What is the smallest possible monetary value of the change she has given you?
Answer next week
#09 The cake and the candles
Solution
The candles and the knife cut are all at random points along the length of the cake. Two of the lines in the diagram below pass through the points where the candles are placed (C), and the other is the line along which Victoria cuts (V). We can鈥檛 tell which is which.
The order of the lines is therefore one of:
C C V
C V C
V C C
The cut divides the candles in one of the three possibilities, so the chance of there being a candle on each piece is 1/3.
Quick Quiz #10
1 According to Guinness World Records, which viscous substance is the subject of the world鈥檚 longest running experiment?
2 Which comic actor played the role of Albert Einstein in the 1994 film I. Q.?
3 What does it mean to have an Erd艖s number of 0?
4 Which Indian kingdom inspired the design of the rockets used by the British against French forces in the Battle of Waterloo in 1815?
5 The last known specimen of which animal died in Cincinnati zoo on 1 September 1914?
Answers below
Quick Quiz #10
Answers
1 Pitch
2 Walter Matthau
3 That you are Paul Erd艖s
4 Mysore
5 Passenger pigeon
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