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.
Take a normal piece of paper, exactly 0.1 mm thick.
Fold it in half, and then in half again, and again, and again.
Do this a total of 50 times.
How thick would the final paper be (if this could be done)?
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Hint: We'll assume that we can actually fold it this many times.
Very thick indeed! The paper doubles in thickness with each fold. If we could fold it 50 times, it would be around 70 million miles thick!
1 fold would be 0.1 + 0.1 = 0.1 x 2 ^ 1 = 0.2 mm
2 folds would be 0.1 + 0.1 + 0.1 + 0.1 = 0.1 x 2 ^ 2 = 0.4 mm
10 folds would be 0.1 x 2 ^ 10 = 102.4 mm
50 folds would be 0.1 x 2 ^ 50 = 112,589,990,684,262.4 mm = 112,589,990.7 km (around 70 million miles).
Using the letters EEEENNNNPPSS complete this grid. The grid reads the same across as down.
...above a concrete floor without breaking the egg?
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Hint: What could cause the egg to break, and how can we prevent this?
If we drop the egg from somewhere above 30 feet high, the egg can fall 30 feet and be caught, whilst still above the floor.