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#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

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triangles colouring algebra 3d shapes probability quadratics routes parabolas shape lines sum to infinity triangle numbers wordplay symmetry square roots dates prime numbers christmas cryptic clues bases number cryptic crossnumbers dodecagons remainders odd numbers arrows speed graphs folding tube maps clocks chalkdust crossnumber irreducible numbers probabilty pascal's triangle time sequences cube numbers logic ellipses multiples books percentages differentiation division fractions perimeter crosswords star numbers coins doubling perfect numbers shapes digits trigonometry planes complex numbers area polygons squares spheres multiplication cards circles mean taxicab geometry numbers people maths coordinates balancing crossnumbers sport integration chess proportion menace rugby dice floors ave factorials regular shapes partitions volume advent palindromes unit fractions sums averages means indices integers hexagons calculus functions surds square numbers 2d shapes chocolate addition games angles scales money grids geometry rectangles factors# Sunday Afternoon Maths LXIV

**Posted on 2018-05-06**

## Equal lengths

The picture below shows two copies of the same rectangle with red and blue lines. The blue line visits the midpoint of the opposite side. The lengths shown in red and blue are of equal length.

What is the ratio of the sides of the rectangle?

## Digitless factor

Ted thinks of a three-digit number. He removes one of its digits to make a two-digit number.

Ted notices that his three-digit number is exactly 37 times his two-digit number. What was Ted's three-digit number?

## Backwards fours

Source: FiveThirtyEight

If A, B, C, D and E are all unique digits, what values would work with the following equation?

$$ABCCDE\times 4 = EDCCBA$$If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVII,

puzzles about algebra, or a random puzzle.

puzzles about algebra, or a random puzzle.