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Puzzle 829
Recently Kevin had a party and because it was his birthday he wanted a mathematical cake!
He ordered a cake in the shape of a cube and had it completely iced (but of course the shop didn't ice the underneath because that just isn't very sensible).
He cut every side of the cake into three equal pieces, giving 27 slices of cake.
He ended up eating all of the pieces of cake that had exactly 2 sides with icing.
So, how many pieces did that leave for the guests?
Answer
Six lots of 4p, 7p, and 19p, and ten lots of 5p, and 12p.
Reasoning
For three denominations of stamps, I was asked to buy 6 of each, and for the other two denominations, I had to buy 10 of each.
So I had to buy at least 6 of all five denominations.
This would be for a total of 6 x (4 + 5 + 7 + 12 + 19) = 282p = £2.82.
The remaining 68p has to buy the remaining 8 stamps, 4 of each of the two remaining denominations.
If we just bought 1 of each of the two remaining denominations they would have cost 68 ÷ 4 = 17p.
So the two remaining denominations must have been 5p and 12p.
Double-Checking 6 x 4 = 24 10 x 5 = 50 6 x 7 = 42 10 x 12 = 120 6 x 19 = 114
For a total of 24 + 50 + 42 + 120 + 114 = 350p = £3.50.
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Puzzle 832
My BrainBashers electronic world atlas has developed another fault, I did a listing of miles from England to particular countries and here is the result:
Chile 800 miles
Wales 4,200 miles
France 1,100 miles
Italy 3,400 miles