Growing Groups
Read the puzzle
Beads are threaded in groups that grow by one bead each time, colours taking turns gold then teal. Beads 1 to 10 are shown: 1 gold, then 2 teal, then 3 gold, then 4 teal. Gold beads are round and teal beads are square. The text adds that 5 gold and 6 teal come next, and so on. Beads 11 to 29 are not shown. Gold or teal: what colour is bead 30?
Groups grow by one bead each time, gold then teal in turn. Beads 11 to 29 are not shown. What colour is bead 30?
Add up 1 + 2 + 3 + ... until you pass 30.
Teal
Groups end at beads 1, 3, 6, 10 ... 28, 36. Bead 30 is in group 8: teal.
How to solve it
Step 1: find where each group ends by adding the group sizes. 1, then 1 + 2 = 3, then 3 + 3 = 6, then 6 + 4 = 10, 10 + 5 = 15, 15 + 6 = 21, 21 + 7 = 28 and 28 + 8 = 36.
Step 2: find the group that holds bead 30. Group 7 ends at bead 28, and group 8 runs from bead 29 to bead 36, so bead 30 is the 2nd bead of group 8.
Step 3: match the group number to its colour. Odd groups (1, 3, 5, 7) are gold and even groups (2, 4, 6, 8) are teal. Group 8 is even, so bead 30 is teal.
The usual wrong answer is gold. Some people skip a group size when adding, which shifts every later boundary. Others stop adding at 28, the end of the gold group 7, and forget that bead 30 is two beads further on.
The answer is teal. Takeaway: the running totals 1, 3, 6, 10, 15, 21, 28, 36 mark where each group ends.
