Openday Problems 1996
prize by
see also openday documents
by the winner
In a tall building the lift is defective.
Only two buttons work.
One always moves the lift up U floors,
if available or else does nothing.
The other always moves it down D floors
if available or else does nothing.
Using the lift it, is possible to go
from the lowest floor, which is ground level 0
to the top floor, which is floor N,
and then return to ground level.
What is the smallest number N could be:
- if D=3 and U=5
- if D=11 and U=15
- for any positive integers D and U,
where 1 is the only positive integer which divides both
- for any positive integers D and U.
Twelve chocolate bars have been distributed
around the globe (a perfect sphere),
each containing a golden ticket.
One bar has been placed at each of the North and South poles.
Another has been placed on the Greenwich meridian
between the North Pole and the equator.
Each chocolate bar lies equidistant from the five bars
closest to it.
Pick any bar which is not on the circle through Greenwich
and the poles, denote its
longitude by g and its latitude by t.
- Make a freehand drawing of the globe indicating the
locations of all the bars.
- Compute g. Compute Cos(g).
- Compute Tan(t).
No decimals in the answer. No tables or calculators to be used.
Page maintained by
jbquig@ucd.ie
Revised 12-Feb-1997.