Spring Teasers

Spring Teaser No 1

One of my neighbours is a maths teacher. He and his wife were sharing diner with us last weekend. My wife (who is also a teacher) asked how many pupils he had in his Year 9 Class. 100 he replied, much to my dearly beloved’s dismay!. 24 boys and 32 girls he added, much to my amusement. What number base system was he talking in?

Cheers

Don

Spring Teaser No 2

My wife had been showing her Year 1 Class different tin cans (don’t ask!). One circular can was as tall as its radius. The other was twice as tall as its diameter. A small (intelligent) ant was crawling from a point on the base rim, along the outer surface of each can to reach the spot on the upper rim, diagonally opposite the starting point. What is the shortest route on each can and what is the ratio of height to radius at which these routes are of equal length?

Cheers

Don

PS I do hope i've recalled this one correctly!

#11 Another set of circles

It’s pretty obvious that the maximum number of different sized circles (excluding infinitely large circles that have become straight lines!) that can be made to 'just touch' one another is four. (each and every circle just touches the other three).

Three circles A, B and C have radii of 1, 2 and 3 respectively. What are the radii of the two 'fourth' circles, that can be made to just touch each of A, B and C. (note the two 'fourth' circles will not touch each other, ‘cos that would break the golden rule!!)

Oh! BTW, there is a standard way and an elegant way to solve this little problem. The normal way will do for most, but in the case of Bam………..

Cheers

Don

#12 Balls in a box (Matthew T)

I have a box 5cm x 5cm x 10cm and spherical balls of diameter 1cm. What is the maximum number of balls can I fit in the box?

All dimensions are exact (internal dimensions for the box) and the box has a lid that must close.

Cheers

Don