Yesterday I was asked to buy some stamps.
In the land of BrainBashers, stamps are available in denominations of 4p, 5p, 7p, 12p, and 19p (just the five different values).
For three denominations of stamps, I was asked to buy six of each. For the other two denominations. I was asked to buy ten of each.
Unfortunately, I forgot which I was supposed to buy six of, and which to buy ten of!
Luckily I had been given the exact money required to buy the stamps, £3.50, so the shopkeeper was able to work out the stamps I needed.
Which stamps did I have to buy?
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Hint
I bought at least 6 of each stamp.
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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