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problem

Fake Gold

7 to 11

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

problem

Rhombus in Rectangle

14 to 16

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

problem

Xtra

14 to 18

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

problem

Home City

7 to 11

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

problem

Favourite

Prime AP

16 to 18

What can you say about the common difference of an AP where every term is prime?

problem

Favourite

Teams

16 to 18

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.

$Mixing \pH$

problem

Favourite

Mixing pH

16 to 18

Use the logarithm to work out these pH values

problem

Favourite

All in a Jumble

11 to 14

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

problem

Scale Draw

5 to 7

Use the grids to draw pictures to different scales.

problem

Favourite

Odds or Sixes?

7 to 11

Play this dice game yourself. How could you make it fair?