Math Quiz
Here are some mathematical puzzles I made up during two nights in which I couldn't find sleep. If you manage to solve all of them, drop me an email with the answers and your name will appear at the Hugi website!
Easy
On her seventh birthday Sue receives 50 coins which she is allowed to spend freely. In the supermarket she notices delicious sweets. Each pack costs 15 coins. Sue buys as many of them as possible. For the remaining money she purchases lollipops - each piece is 2 coins. With how many packs of sweets, lollipops and coins will Sue return home?
Medium
Several years ago I met a woman at a party that took place in the evening before New Year's Day. She told me about her life: "At the age of 24 I married John, who was born in the year 1952. A year later our family was enriched by our first child, and after another two years our second child saw the light of the day. Oh, how many things have changed since then! Now the sum of the kids' ages is 10 years." After a short pause I made this remark: "Funny! Had you computed the sum of the ages of all your family members (your husband, your two children and yourself) three years ago, you'd have got a total of 70 years." I did not meet this woman again until recently, on the evening before January 1st, 2001. How old was she then? (All ages are positive integer numbers.)
Hard
The side a of a triangular fence has a length of 3 metres, the side b a length of 2 metres. Regarding the angles of the triangle we know these facts: sin(alpha) = cos(beta) and sin(beta) > cos(alpha). How long is the fence (i.e., the perimeter of the triangle)? (a is the opposite side of alpha, b is the opposite side of beta; the third angle can be called gamma and its opposite side c.)