Choose two digits and arrange them to make two double-digit
numbers. Now add your double-digit numbers. Now add your single
digit numbers. Divide your double-digit answer by your single-digit
answer. Try lots of examples. What happens? Can you explain it?
What are the missing numbers in the pyramids?
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.
According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
What rectangular boxes, with integer sides, have their surface
areas equal to their volumes? One example is $4$ by $6$ by
How to do this? No doubt different people will suggest different
methods. Suppose the dimensions of the box are $a$, $b$ and $c$
units where $a \leq b \leq c$ . You might like to show that the
problem amounts to solving the equation$1 = 2/a + 2/ b + 2/c$ and
then show $3 \leq a\leq 6 , 3 \leq b \leq 12 , 3 \leq c \leq