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Burning Down

One night two candles, one of which was 3 cm longer than the other were lit. The longer one was lit at 5.30 pm and the shorter one at 7 pm. At 9.30 pm they were both the same length. The longer one, burned out at 11.30 pm and the shorter one burned out at 11 pm. How long was each candle originally?

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Fair Shares?

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

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A Method of Defining Coefficients in the Equations of Chemical Reactions

A simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations.

A Problem of Time

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

"It was the best butter," the March Hare meekly replied.
"Yes, but some crumbs must have got in as well," the Hatter grumbled: "you shouldn't have put it in with the bread-knife."
The March Hare took the watch and looked at it gloomily: then he dipped it into his cup of tea, and looked at it again: but he could think of nothing better to say than his first remark, "It was the best butter, you know."

Tea Party

Consider a watch face which has all the hours shown by the same mark, and both hands the same in length and shape. It is opposite to a mirror. Find the time between 6 and 7 when the time as read direct and in the mirror is exactly the same.