Bead 50
Read the puzzle
Beads are threaded on a string. Beads 1 to 10 are shown: gold, gold, teal, violet, gold, gold, teal, violet, gold, gold. Gold beads are round, teal are square, violet are diamonds. The pattern gold, gold, teal, violet repeats. Beads 11 to 49 are not shown. The colour choices are gold, teal and violet. What colour is bead 50?
Beads 11 to 49 are not shown. The pattern gold, gold, teal, violet repeats. What colour is bead 50?
Count in groups of 4.
Gold
50 = 12 × 4 + 2: the 2nd bead of the pattern, gold.
How to solve it
Step 1: find the true length of the repeat. There are only three colours, but the block is gold, gold, teal, violet, which is 4 beads long because gold appears twice.
Step 2: divide the bead number by 4. 50 divided by 4 is 12 with remainder 2, since 12 x 4 = 48 and 50 - 48 = 2. Beads 1 to 48 make twelve full blocks, so bead 50 is the 2nd bead of the next block.
Step 3: read position 2 from the block. Position 1 is gold, position 2 is gold, position 3 is teal, position 4 is violet. Bead 50 is gold.
Check from the end of a block: bead 48 is violet (the 4th of its block), bead 49 is gold, and bead 50 is gold again.
The usual wrong answer is teal. It comes from counting three colours instead of four beads, then working out 50 divided by 3, which leaves remainder 2, and reading the 2nd colour in the list gold, teal, violet.
The answer is gold. Takeaway: always count beads in the repeat, not different colours.
