Schools Mathematics Grand Challenge
PROBLEM 1
Mary recently won 1,000 Euro in a local lottery competition and
wishes to invest it for 5 years (60 months). She has spoken to 6
banks and each of them has offered her a slightly different deal
on interest payments. The offers from the six banks were:
- Bank 1: 30% interest every 60 months
- Bank 2: 15% interest every 30 months
- Bank 3: 10% interest every 20 months
- Bank 4: 7.5% interest every 15 months
- Bank 5: 6% interest every 12 months
- Bank 6: 5% interest every 10 months
For instance, if she invested with Bank 2 she would receive: 150
Euro interest after the first 30 months, giving her a total of 1150
Euro; after another 30 months (at the end of 60 months) she would
receive 15% interest on her 1150 Euro, which is 172.50 Euro, giving
her a total of 1150 + 172.50 = 1322.50 Euro at the end of the 60
months.
Which bank will pay Mary the most interest over the 60 month period?
Please give your answer as a number from 1 to 7 (inclusive). If you
think all banks offer the same deal, give the number 7 as your
answer, otherwise your answer should be the number of the bank
offering the best deal.
PROBLEM 2
Currently there are 7 days in a week and 365 days in a standard (non-leap)
year. This means that the number of weeks in a standard (non-leap)
year is not a whole number: in fact it is approximately 52.1429. It is
proposed to change the number of days in a week so that the following
conditions are satisfied:
- The number of weeks in a standard (non-leap) year is a whole number;
- The number of days in a week is a whole number;
- A week cannot contain just 1 day;
- A week cannot be 365 days long.
How many different possibilities are there for the length of a week
under this scheme?
PROBLEM 3
John, Sheila and Mark meet at the bus-stop on a winter's morning.
John is wearing a blue jacket, Sheila is wearing a black jacket, and
Mark is wearing a red jacket. One of the three friends says:
"I am wearing a blue hat, one of you is wearing a red hat, and the other
is wearing a black hat. But none of us is wearing a hat that matches
the colour of our jacket."
Sheila then replies to him:
"You're absolutely correct."
What colour hat is Mark wearing? If you think his hat is
black, then submit 1 as your answer; if you think the hat is
blue, then submit 2 as your answer; if you think the hat is
red, then submit 3 as your answer.
NOTE: All of the three friends speak the truth.
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