# Millennium Problems

 From: Basil Reid Date: 18 December 1999 Subject: Millennium Problems I need some maths problems to set my classes based on the number 2000. Have you got any ideas?

### Maths Help suggests:

Here are some tasks you could set. We are glad you only asked for problems, not for the solutions!!

(1) A child is born as the clock strikes midnight at the turn of the millennium. How old will the child be 2000 days, 2000 hours and 2000 minutes later?

(2) How can you make the answer 2000 by only using the digit 2 and the four operations + , - , × , ÷ and brackets? Try to find a way which uses 2 the least number of times.

(3) Perhaps you spotted the "obvious" way to do Question (2). But can you do the same thing, make an answer of 2000, but only using the digit 3, the digit 4, and so on up to 9?

(4) Write down a sequence of 10 numbers which follow a rule. The LAST number (10th term) in the sequence must be 2000. How many sequences using different types of rule can you find?
EXAMPLE: 1955, 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000
using the rule "add 5 to each term to get the next term".

(5) A sugar cube measures 1cm by 1cm by 1cm. You have to pack 2000 into a box. What will the dimensions of the box be if it is to have minimum surface area (so that there is less chance of the sugar getting damp)?

(6) My grandmother, who was born in 1900, remembers the days when a pound was made up of 20 shillings, and a shilling was made up of 12 old pennies. If she saved 2000 old pennies, how much money would she have in our present system?

(7) On 1st January 2000, Alfie starts a savings scheme with his uncle. Alfie promises to put one pound into a pot on the first day of each month, and at the end of the month his uncle will add to the pot an amount equal to whatever is in the pot, plus an extra pound. How much will there be in the pot on 31st December 2000 (for Alfie to celebrate the "real" millennium)?