In the olden days, many moons ago, the wealthy used to have an something called an 'Eight Day' clock. These were quite reliable and well made. How long were they originally designed to go without winding?
Hint: There is a little trick in the question.
They did not work at all without winding, but once wound, they would continue to tick for about 8 days.
I have three children.
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.
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)?
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.