Bead 20
Read the puzzle
Beads are threaded on a string. Beads 1 to 7 are shown: red round, green square, blue diamond, red, green, blue, red. The pattern red, green, blue repeats along the string. Beads 8 to 19 are not shown. The colour choices are red, green and blue. What colour is bead 20?
Beads 8 to 19 are not shown. The pattern red, green, blue repeats. What colour is bead 20?
Count in groups of 3.
Green
20 = 6 × 3 + 2: bead 20 is the 2nd colour, green.
How to solve it
Step 1: find the length of the repeat. Red, green, blue is a block of 3 beads, so the colours come back every 3 beads.
Step 2: divide the bead number by the block length. 20 divided by 3 is 6 with remainder 2, because 6 x 3 = 18 and 20 - 18 = 2. So beads 1 to 18 make six full blocks, and bead 20 is the 2nd bead of the next block.
Step 3: read that position from the pattern. Position 1 is red, position 2 is green, position 3 is blue. So bead 20 is green.
You can confirm it by listing the red beads: 1, 4, 7, 10, 13, 16, 19. Bead 19 is red, so bead 20, the next one, is green.
The usual wrong answer is red, from treating 20 as a fresh start because it is a round number, or blue, from counting the remainder from the end of the block instead of the start. The pattern does not care about tens; it restarts every 3.
The answer is green. Takeaway: remainder 1 means the first colour, remainder 2 the second, and remainder 0 the last.
