快猫短视频

#64 Matching tiles

Set by Colin Beveridge

A game is played with a set of tiles. Each tile is one of three shapes (circle, triangle or square), is one of three colours (red, blue or yellow), is one of three sizes (small, medium or large), is one of three textures (smooth, rough or ridged), and has one of three letters on it (A, B or C).

Given that each combination of attributes is used on exactly one tile, how many tiles are there?

A meld consists of three tiles in any order, such that each attribute is either the same on all three tiles or different on all three. For example, the big, red, rough circle labelled A; the small, red, smooth square labelled A; and the medium, red, ridged triangle labelled A form a meld. How many melds include the big, red, rough circle labelled A?

How many possible melds are there?

Solution next week

#63 A 2025 puzzle

Solution

The number 3025 also works: (30 + 25)² = 55² = 3025.

If a square number ends in a 1, it must be the square of a number ending in 1 or 9.

The only other four-digit number with the split-sum-square property is 9801, since (98 + 1)² = 99² = 9801.