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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

Square and cube endings

List of all puzzles

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

puzzles about palindromes, or a random puzzle.