Brainteasers

10th June 2005 at 01:00
Puzzles to test mathematical skills, set by Anita Straker. Solutions below More brainteasers on www.tes.co.ukteacherbrainteasers

AT THE MARKET

Mrs Jones bought eight items at the market for a total cost of between pound;1 and pound;10.

The amount she spent in pence was a multiple of 8, and the sum of its three digits was a multiple of 8.

Mrs Jones gave the stall holder some pound;1 coins to pay for his items.

The change she got in pence was also a multiple of 8.

How much change did Mrs Jones get?

GEOMETRY PUZZLE

In the diagram, AD is parallel to BC, BD is perpendicular to DC, and AE is perpendicular to BD. AB is 41cm, AD is 50cm and BF is 9cm.

What is the area of quadrilateral DCEF?

SOLUTIONS

At the market (ages 8 - 12). 48p or 88p. There are only five 3-digit numbers that are multiples of 8 and have a digit sum of 8. These are 152 (pound;1 coin, 48p change); 224 (three pound;1 coins, 78p change); 440 (five pound;1 coins, 60p change); 512 (six pound;1 coins, 88p change); 800 (eight pound;1 coins, no change). Geometry puzzle (ages 14 - 16) The area of DCEF is 960cm2. Using Pythagoras, AF = 40cm and FD = 30cm. Triangles ADF and BFE are similar, so FE is 12cm. BD = BF + FD = 39cm. Triangles BDC and BFE are similar, so DC is 52cm. DCEF is a trapezium with height DF. Area of DCEF is ((FE + DC) x FD) 2 = 960cm2.

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