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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

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

puzzles about complex numbers, or a random puzzle.