Bead 100
Read the puzzle
Beads are threaded on a string. Beads 1 to 12 are shown: teal, teal, gold, gold, gold, teal, teal, gold, gold, gold, teal, teal. Teal beads are square and gold beads are round. The pattern teal, teal, gold, gold, gold repeats. Beads 13 to 99 are not shown. The colour choices are teal and gold. What colour is bead 100?
Beads 13 to 99 are not shown. The pattern teal, teal, gold, gold, gold repeats. What colour is bead 100?
Count in groups of 5.
Gold
100 = 19 × 5 + 5: bead 100 is the 5th bead of its group, and the 5th is gold.
How to solve it
Step 1: the repeating block is teal, teal, gold, gold, gold, which is 5 beads long.
Step 2: divide the bead number by 5. 100 divided by 5 is exactly 20 with remainder 0, since 20 x 5 = 100. A remainder of 0 means bead 100 is the last bead of the 20th block, the same as saying 100 = 19 x 5 + 5, the 5th bead of its block.
Step 3: read position 5 from the block. Positions 1 and 2 are teal; positions 3, 4 and 5 are gold. So bead 100 is gold.
Check by counting back: beads 96 and 97 start a block and are teal, then 98, 99 and 100 are gold.
The usual wrong answer is teal. A remainder of 0 tempts people to read position 1, as if the pattern starts again at bead 100. In fact the block ends there, and the new block starts at bead 101.
The answer is gold. Takeaway: when the bead number divides exactly, take the last bead of the block, not the first.
