# September 2002, Stage 3&4

## Problems

##### Age 7 to 14 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

##### Age 7 to 16 Challenge Level:

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

##### Age 11 to 14 Challenge Level:

A triangle ABC resting on a horizontal line is "rolled" along the
line. Describe the paths of each of the vertices and the
relationships between them and the original triangle.

##### Age 11 to 14 Challenge Level:

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. . . .

##### Age 11 to 14 Challenge Level:

There are two forms of counting on Vuvv - Zios count in base 3 and
Zepts count in base 7. One day four of these creatures, two Zios
and two Zepts, sat on the summit of a hill to count the legs of. . . .

##### Age 14 to 16 Challenge Level:

Find the five distinct digits N, R, I, C and H in the following
nomogram

##### Age 14 to 16 Challenge Level:

How many different ways can you arrange the officers in a square?

##### Age 14 to 16 Challenge Level:

An equilateral triangle is constructed on BC. A line QD is drawn,
where Q is the midpoint of AC. Prove that AB // QD.

##### Age 14 to 16 Challenge Level:

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

##### Age 14 to 16 Challenge Level:

Can you create a Latin Square from multiples of a six digit number?

##### Age 14 to 16 Challenge Level:

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

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