Step 1 of 10Decode
Each counter carries one signed unit.
Decode
Pair
Count
Add zero
Zero-Pair Sorter
Counter code
+
Yellow counter
+1
−
Red counter
−1
(+1) + (−1) = 0
Load → Pair → Read
Yellow · +1 each
+
+
+
+
+
+
→
Red · −1 each
−
−
Zero-pair bay
+
+
−
0
+
+
−
0
Remove 1 yellow and 1 red together
6 − 2
→
5 − 1
→
4 − 0
= +4
+
+
+
+
survivors+4
positive − negative
6 − 2 = +4−4
0
+4
One value · many models
Target: +3
Adding a zero pair changes the look, not the value.
Adding a zero pair changes the look, not the value.
Fewest tiles
+
+
+
3 − 0 = +3
Add 1 zero pair
+
+
+
+
−
4 − 1 = +3
Same difference → same integer
Build −3 with exactly 7
Start with the value.
Three red counters make −3. Four slots are still open.
Three red counters make −3. Four slots are still open.
−
−
−
+
−
+
−
+
+
−
0
+
+
−
0
Count
2 + 5 = 7 tiles
2 + 5 = 7 tiles
Value
2 − 5 = −3
2 − 5 = −3
2 yellow + 5 red
Your model · −6 with 10
Fill every slot.
Your model must have value −6 and use exactly 10 tiles.
Your model must have value −6 and use exactly 10 tiles.
Check both: total tiles and signed value.
Use your whiteboard.Draw exactly 10 counters for −6. Circle every zero pair, then submit.
Work submitted — model unlocked.
Sorter receipt · −6 with 10
Start with 6 red.
Four spaces remain, so add two zero pairs.
Four spaces remain, so add two zero pairs.
−
−
−
−
−
−
+
−
+
−
+
+
−
0
+
+
−
0
remove 2 zero pairs
−
−
−
−
−
−
Yellow − red: 2 − 8 = −6
2 yellow + 8 red = −6
+ / −
You can build any integer.
Read the counters, cancel zero, and check the count.
+1 / −1Decode each color
0Match zero pairs
leftCount survivors
+ zeroBuild another model
Exact-count check: yellow + red = total tiles · Value check: yellow − red = integer