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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:
Australia 500 miles
Peru 8,000 miles
India 4,500 miles
Scotland 9,500 miles
One is the same age as the first number in my age, another is the same age as the second number in my age, and the third is the same age as the sum of the two numbers in my age.
None of the children are the same age and the total of our ages is 45. How old am I?
As my children are different ages, the lowest they could be is 1, 2, 3, and as our ages add to 45 this would make me 39. Working backwards the only answer to make the sum correct is 27 + 2 + 7 + 9 = 45.
Alternatively, we could use algebra and say that I am 10A + B years of age. My children are A, B and A+B years of age. Our ages add to 45, so:
10A + B + A + B + A+B = 45
Collecting like terms together gives:
12A + 3B = 45
Dividing throughout by 3 gives:
4A + B = 15
If A = 1 then B would be 11, which makes no sense for an age. If A = 2 then B = 7 and as all values that work give us a correct answer. So I am 27.
Note how A = 3 would make B = 3, which isn't allowed. And A > 3 will take us past 15, so there can be no other solutions.
Puzzle 12
Daft Dave, our local DIY expert, is renovating the local hospital.
He has to number each of the rooms in the hospital with plastic numbers.
However, he has run out of the number 9.
How many 9's must Dave buy in order to number all 1,000 rooms?
We then repeat this for 100, 200, 300, up to 900  which is 200 9's.
But from 900 to 999 we have an extra 100 9's as each starts with a 9.
So the total is 300.
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