Volume 34
, Issue 2


Experiment 1: Figure 1(a) shows a portion of tape which has been folded using the $D^1U^1$-procedure, with the first few (say 10) triangles cut away.

In Part 1 (Parabola Vol. 34, No 1) we introduced you to a basic construction whereby we folded down m times at the top of a tape and folded up n times at the bottom of the tape (see Figure 1).

Semi-definite optimization is a very new topic in the branch of applied mathematics known as optimization. Optimization refers to the process of finding the best way of achieving a goal.

Let $x, y$ and $z$ be integers. Prove that if $2x + 4y + 5z$ is a multiple of $17$, then so is $3x + 6y − z$.

Q.1025 Find the smallest number that when divided by $29$ leaves the remainder $23$ and that when divided by $37$ leaves the remainder $31$.

Q.1015 Quantities of coins are available denominated at one tenth, one twelveth and one sixteenth of a penny. How can these be used to settle a debt of one two hundred and fortieth of a penny? The giving of change is allowed.