diff --git a/src/App.tsx b/src/App.tsx
index 5b3da99..0f42d15 100644
--- a/src/App.tsx
+++ b/src/App.tsx
@@ -56,6 +56,7 @@ import SubtractionGamePage from './pages/SubtractionGamePage';
 import StackingBlocksPage from './pages/StackingBlocksPage';
 import ParityBitsGamePage from './pages/ParityBitsGamePage';
 import CrapsGamePage from './pages/CrapsGamePage';
+import NeighborSumAvoidancePage from './pages/NeighborSumAvoidancePage';
 
 const queryClient = new QueryClient();
 
@@ -81,6 +82,7 @@ const App = () => (
           <Route path="/themes/discrete-math/structures" element={<Structures />} />
           <Route path="/themes/discrete-math/numbers" element={<Numbers />} />
           <Route path="/themes/discrete-math/graphs" element={<Graphs />} />
+          <Route path="/themes/discrete-math/graphs/neighbor-sum-avoidance" element={<NeighborSumAvoidancePage />} />
           <Route path="/themes/social-choice" element={<SocialChoice />} />
           <Route path="/themes/advanced-algorithms" element={<AdvancedAlgorithms />} />
           <Route path="/themes/data-structures" element={<DataStructures />} />
diff --git a/src/components/NeighborSumAvoidance.tsx b/src/components/NeighborSumAvoidance.tsx
new file mode 100644
index 0000000..fbcd5b4
--- /dev/null
+++ b/src/components/NeighborSumAvoidance.tsx
@@ -0,0 +1,373 @@
+import { useState, useEffect, useRef } from 'react';
+import { Card, CardContent, CardDescription, CardHeader, CardTitle } from '@/components/ui/card';
+import { Button } from '@/components/ui/button';
+import { Switch } from '@/components/ui/switch';
+import { Label } from '@/components/ui/label';
+import { Timer, RotateCcw } from 'lucide-react';
+import confetti from 'canvas-confetti';
+import { toast } from 'sonner';
+import SocialShare from '@/components/SocialShare';
+
+interface NeighborSumAvoidanceProps {
+  showSocialShare?: boolean;
+}
+
+const NeighborSumAvoidance = ({ showSocialShare = false }: NeighborSumAvoidanceProps) => {
+  const [mode, setMode] = useState<'default' | 'guided'>('default');
+  const [isActive, setIsActive] = useState(false);
+  const [slots, setSlots] = useState<(number | null)[]>(Array(9).fill(null));
+  const [availableNumbers, setAvailableNumbers] = useState<number[]>([1, 2, 3, 4, 5, 6, 7, 8, 9]);
+  const [draggedNumber, setDraggedNumber] = useState<number | null>(null);
+  const [draggedFrom, setDraggedFrom] = useState<number | null>(null);
+  const [draggedSlot, setDraggedSlot] = useState<number | null>(null);
+  const [time, setTime] = useState(0);
+  const [swaps, setSwaps] = useState(0);
+  const [isComplete, setIsComplete] = useState(false);
+  const timerRef = useRef<NodeJS.Timeout | null>(null);
+
+  useEffect(() => {
+    if (isActive && !isComplete) {
+      timerRef.current = setInterval(() => {
+        setTime(t => t + 1);
+      }, 1000);
+    } else if (timerRef.current) {
+      clearInterval(timerRef.current);
+    }
+    return () => {
+      if (timerRef.current) clearInterval(timerRef.current);
+    };
+  }, [isActive, isComplete]);
+
+  const isDivisible = (a: number, b: number) => {
+    const sum = a + b;
+    return sum % 3 === 0 || sum % 5 === 0 || sum % 7 === 0;
+  };
+
+  const getViolations = () => {
+    const violations: number[] = [];
+    for (let i = 0; i < 9; i++) {
+      const current = slots[i];
+      const next = slots[(i + 1) % 9];
+      if (current !== null && next !== null && isDivisible(current, next)) {
+        violations.push(i);
+      }
+    }
+    return violations;
+  };
+
+  const checkWin = () => {
+    if (slots.every(s => s !== null) && getViolations().length === 0) {
+      setIsComplete(true);
+      confetti({
+        particleCount: 100,
+        spread: 70,
+        origin: { y: 0.6 }
+      });
+      toast.success(`Congratulations! Completed in ${formatTime(time)}${mode === 'guided' ? ` with ${swaps} swaps` : ''}!`);
+    }
+  };
+
+  useEffect(() => {
+    if (isActive) {
+      checkWin();
+    }
+  }, [slots, isActive]);
+
+  const formatTime = (seconds: number) => {
+    const mins = Math.floor(seconds / 60);
+    const secs = seconds % 60;
+    return `${mins}:${secs.toString().padStart(2, '0')}`;
+  };
+
+  const startGame = (selectedMode: 'default' | 'guided') => {
+    setMode(selectedMode);
+    setIsActive(true);
+    setTime(0);
+    setSwaps(0);
+    setIsComplete(false);
+
+    if (selectedMode === 'default') {
+      setSlots(Array(9).fill(null));
+      setAvailableNumbers([1, 2, 3, 4, 5, 6, 7, 8, 9]);
+    } else {
+      // Guided mode: random arrangement
+      const shuffled = [...Array(9)].map((_, i) => i + 1).sort(() => Math.random() - 0.5);
+      setSlots(shuffled);
+      setAvailableNumbers([]);
+    }
+  };
+
+  const restart = () => {
+    setIsActive(false);
+    setIsComplete(false);
+    setSlots(Array(9).fill(null));
+    setAvailableNumbers([1, 2, 3, 4, 5, 6, 7, 8, 9]);
+    setTime(0);
+    setSwaps(0);
+  };
+
+  const handleDragStart = (num: number, fromSlot: number | null) => {
+    setDraggedNumber(num);
+    setDraggedFrom(fromSlot);
+  };
+
+  const handleDrop = (toSlot: number) => {
+    if (draggedNumber === null) return;
+
+    if (mode === 'default') {
+      // Default mode: place number in slot
+      const newSlots = [...slots];
+      newSlots[toSlot] = draggedNumber;
+      setSlots(newSlots);
+      setAvailableNumbers(availableNumbers.filter(n => n !== draggedNumber));
+    } else {
+      // Guided mode: swap numbers
+      if (draggedFrom !== null && draggedFrom !== toSlot) {
+        const newSlots = [...slots];
+        const temp = newSlots[toSlot];
+        newSlots[toSlot] = newSlots[draggedFrom];
+        newSlots[draggedFrom] = temp;
+        setSlots(newSlots);
+        setSwaps(s => s + 1);
+      }
+    }
+
+    setDraggedNumber(null);
+    setDraggedFrom(null);
+  };
+
+  const handleSlotClick = (slotIndex: number) => {
+    if (mode === 'default') {
+      // Remove from slot in default mode
+      if (slots[slotIndex] !== null) {
+        setAvailableNumbers([...availableNumbers, slots[slotIndex]!].sort((a, b) => a - b));
+        const newSlots = [...slots];
+        newSlots[slotIndex] = null;
+        setSlots(newSlots);
+      }
+    } else if (mode === 'guided') {
+      // Swap in guided mode
+      if (draggedSlot === null) {
+        setDraggedSlot(slotIndex);
+      } else if (draggedSlot !== slotIndex) {
+        const newSlots = [...slots];
+        const temp = newSlots[slotIndex];
+        newSlots[slotIndex] = newSlots[draggedSlot];
+        newSlots[draggedSlot] = temp;
+        setSlots(newSlots);
+        setSwaps(s => s + 1);
+        setDraggedSlot(null);
+      } else {
+        setDraggedSlot(null);
+      }
+    }
+  };
+
+  const renderCircle = () => {
+    const radius = 150;
+    const centerX = 200;
+    const centerY = 200;
+    const violations = getViolations();
+
+    return (
+      <svg width="400" height="400" className="mx-auto">
+        {/* Draw circle */}
+        <circle cx={centerX} cy={centerY} r={radius} fill="none" stroke="hsl(var(--border))" strokeWidth="2" />
+        
+        {/* Draw violation arcs */}
+        {violations.map(i => {
+          const angle1 = (i * 360 / 9 - 90) * Math.PI / 180;
+          const angle2 = ((i + 1) * 360 / 9 - 90) * Math.PI / 180;
+          const x1 = centerX + radius * Math.cos(angle1);
+          const y1 = centerY + radius * Math.sin(angle1);
+          const x2 = centerX + radius * Math.cos(angle2);
+          const y2 = centerY + radius * Math.sin(angle2);
+          
+          return (
+            <path
+              key={i}
+              d={`M ${x1} ${y1} A ${radius} ${radius} 0 0 1 ${x2} ${y2}`}
+              fill="none"
+              stroke="hsl(var(--destructive))"
+              strokeWidth="4"
+            />
+          );
+        })}
+
+        {/* Draw edges in guided mode */}
+        {mode === 'guided' && slots.every(s => s !== null) && slots.map((num1, i) => {
+          return slots.slice(i + 1).map((num2, j) => {
+            const idx2 = i + j + 1;
+            if (num1 !== null && num2 !== null && !isDivisible(num1, num2)) {
+              const angle1 = (i * 360 / 9 - 90) * Math.PI / 180;
+              const angle2 = (idx2 * 360 / 9 - 90) * Math.PI / 180;
+              const x1 = centerX + radius * Math.cos(angle1);
+              const y1 = centerY + radius * Math.sin(angle1);
+              const x2 = centerX + radius * Math.cos(angle2);
+              const y2 = centerY + radius * Math.sin(angle2);
+              
+              // Check if this forms part of the cycle (adjacent positions on circle)
+              const isAdjacentOnCircle = Math.abs(i - idx2) === 1 || Math.abs(i - idx2) === 8;
+              
+              return (
+                <line
+                  key={`${i}-${idx2}`}
+                  x1={x1}
+                  y1={y1}
+                  x2={x2}
+                  y2={y2}
+                  stroke={isAdjacentOnCircle ? "hsl(var(--primary))" : "hsl(var(--muted-foreground))"}
+                  strokeWidth={isAdjacentOnCircle ? "2" : "1"}
+                  opacity={isAdjacentOnCircle ? "0.8" : "0.3"}
+                />
+              );
+            }
+            return null;
+          });
+        })}
+        
+        {/* Draw slots */}
+        {slots.map((num, i) => {
+          const angle = (i * 360 / 9 - 90) * Math.PI / 180;
+          const x = centerX + radius * Math.cos(angle);
+          const y = centerY + radius * Math.sin(angle);
+          
+          const isSelected = mode === 'guided' && draggedSlot === i;
+          
+          return (
+            <g key={i}>
+              <circle
+                cx={x}
+                cy={y}
+                r="25"
+                fill={isSelected ? "hsl(var(--primary))" : "hsl(var(--background))"}
+                stroke={isSelected ? "hsl(var(--primary))" : "hsl(var(--border))"}
+                strokeWidth="2"
+                onDragOver={(e) => e.preventDefault()}
+                onDrop={() => handleDrop(i)}
+                onClick={() => handleSlotClick(i)}
+                className="cursor-pointer"
+              />
+              {num !== null && (
+                <text
+                  x={x}
+                  y={y}
+                  textAnchor="middle"
+                  dominantBaseline="middle"
+                  className="text-xl font-bold select-none pointer-events-none"
+                  fill={isSelected ? "hsl(var(--primary-foreground))" : "hsl(var(--foreground))"}
+                >
+                  {num}
+                </text>
+              )}
+            </g>
+          );
+        })}
+      </svg>
+    );
+  };
+
+  return (
+    <div className="container mx-auto px-4 py-8">
+      <Card>
+        <CardHeader>
+          <CardTitle>Neighbor Sum Avoidance</CardTitle>
+          <CardDescription>
+            Can you arrange the numbers 1-9 in a circle so that the sum of two neighbors is never divisible by 3, 5, or 7?
+          </CardDescription>
+        </CardHeader>
+        <CardContent className="space-y-6">
+          {!isActive ? (
+            <div className="space-y-6">
+              <div className="flex items-center justify-center gap-4">
+                <Label htmlFor="mode-switch">Default Mode</Label>
+                <Switch
+                  id="mode-switch"
+                  checked={mode === 'guided'}
+                  onCheckedChange={(checked) => setMode(checked ? 'guided' : 'default')}
+                />
+                <Label htmlFor="mode-switch">Guided Mode</Label>
+              </div>
+
+              <div className="space-y-4 text-center">
+                <div className="text-sm text-muted-foreground space-y-2">
+                  {mode === 'default' ? (
+                    <>
+                      <p>Drag numbers from below into the circle slots.</p>
+                      <p>Adjacent numbers that sum to a multiple of 3, 5, or 7 will show a red arc.</p>
+                      <p>Click a filled slot to remove the number.</p>
+                    </>
+                  ) : (
+                    <>
+                      <p>Numbers are connected by edges if their sum is NOT divisible by 3, 5, or 7.</p>
+                      <p>Click two slots to swap their numbers and form a cycle on the circle's edge.</p>
+                    </>
+                  )}
+                </div>
+                <Button onClick={() => startGame(mode)} size="lg">
+                  Start {mode === 'default' ? 'Default' : 'Guided'} Mode
+                </Button>
+              </div>
+            </div>
+          ) : (
+            <div className="space-y-6">
+              <div className="flex items-center justify-between">
+                <div className="flex items-center gap-2">
+                  <Timer className="w-4 h-4" />
+                  <span className="font-mono">{formatTime(time)}</span>
+                </div>
+                {mode === 'guided' && (
+                  <div className="text-sm text-muted-foreground">
+                    Swaps: {swaps}
+                  </div>
+                )}
+                <Button variant="outline" size="sm" onClick={restart}>
+                  <RotateCcw className="w-4 h-4 mr-2" />
+                  Restart
+                </Button>
+              </div>
+
+              {renderCircle()}
+
+              {mode === 'default' && availableNumbers.length > 0 && (
+                <div className="flex flex-wrap justify-center gap-4">
+                  {availableNumbers.map(num => (
+                    <div
+                      key={num}
+                      draggable
+                      onDragStart={() => handleDragStart(num, null)}
+                      className="w-12 h-12 rounded-full border-2 border-primary bg-background flex items-center justify-center text-lg font-bold cursor-move hover:scale-110 transition-transform"
+                    >
+                      {num}
+                    </div>
+                  ))}
+                </div>
+              )}
+
+              {isComplete && (
+                <div className="text-center space-y-4">
+                  <p className="text-lg font-semibold text-primary">
+                    🎉 Congratulations! You solved it in {formatTime(time)}
+                    {mode === 'guided' && ` with ${swaps} swaps`}!
+                  </p>
+                  <Button onClick={restart}>Play Again</Button>
+                </div>
+              )}
+            </div>
+          )}
+        </CardContent>
+      </Card>
+      {showSocialShare && (
+        <div className="mt-8">
+          <SocialShare
+            url={window.location.href}
+            title="Neighbor Sum Avoidance - Interactive Graph Puzzle"
+            description="Can you arrange numbers 1-9 in a circle avoiding forbidden sums?"
+          />
+        </div>
+      )}
+    </div>
+  );
+};
+
+export default NeighborSumAvoidance;
diff --git a/src/pages/NeighborSumAvoidancePage.tsx b/src/pages/NeighborSumAvoidancePage.tsx
new file mode 100644
index 0000000..3a14633
--- /dev/null
+++ b/src/pages/NeighborSumAvoidancePage.tsx
@@ -0,0 +1,11 @@
+import NeighborSumAvoidance from "@/components/NeighborSumAvoidance";
+
+const NeighborSumAvoidancePage = () => {
+  return (
+    <div className="min-h-screen bg-background">
+      <NeighborSumAvoidance showSocialShare={true} />
+    </div>
+  );
+};
+
+export default NeighborSumAvoidancePage;
diff --git a/src/pages/theme-pages/discrete-math/Graphs.tsx b/src/pages/theme-pages/discrete-math/Graphs.tsx
index f6a9ea6..c033615 100644
--- a/src/pages/theme-pages/discrete-math/Graphs.tsx
+++ b/src/pages/theme-pages/discrete-math/Graphs.tsx
@@ -1,11 +1,115 @@
-import ComingSoon from "@/components/ComingSoon";
+import { Card, CardContent, CardDescription, CardHeader, CardTitle } from '@/components/ui/card';
+import { Search } from 'lucide-react';
+import { Input } from '@/components/ui/input';
+import { Badge } from '@/components/ui/badge';
+import Layout from '@/components/Layout';
+import { useState } from 'react';
+import NeighborSumAvoidance from '@/components/NeighborSumAvoidance';
+
+interface Interactive {
+  id: string;
+  title: string;
+  description: string;
+  tags: string[];
+  component: React.ComponentType<{ showSocialShare?: boolean }>;
+}
+
+const interactives: Interactive[] = [
+  {
+    id: 'neighbor-sum-avoidance',
+    title: 'Neighbor Sum Avoidance',
+    description: 'Arrange numbers 1-9 in a circle so that the sum of two neighbors is never divisible by 3, 5, or 7. Two modes: default and guided!',
+    tags: ['graphs', 'cycles', 'constraints', 'puzzle', 'graph-theory'],
+    component: NeighborSumAvoidance
+  },
+];
 
 const Graphs = () => {
+  const [searchTerm, setSearchTerm] = useState('');
+  const [selectedInteractive, setSelectedInteractive] = useState<Interactive | null>(null);
+
+  const filteredInteractives = interactives.filter(interactive =>
+    interactive.title.toLowerCase().includes(searchTerm.toLowerCase()) ||
+    interactive.description.toLowerCase().includes(searchTerm.toLowerCase()) ||
+    interactive.tags.some(tag => tag.toLowerCase().includes(searchTerm.toLowerCase()))
+  );
+
+  if (selectedInteractive) {
+    const InteractiveComponent = selectedInteractive.component;
+    return (
+      <div className="min-h-screen bg-background">
+        <div className="container mx-auto px-4 py-8 space-y-6">
+          <div className="flex items-center gap-4">
+            <button
+              onClick={() => setSelectedInteractive(null)}
+              className="text-primary hover:text-primary/80 font-medium"
+            >
+              ← Back to Graphs
+            </button>
+          </div>
+          <InteractiveComponent showSocialShare={true} />
+        </div>
+      </div>
+    );
+  }
+
   return (
-    <ComingSoon 
-      title="Graphs"
-      description="Discover graph theory, algorithms on graphs, trees, and network analysis through interactive graph manipulation and visualization tools."
-    />
+    <Layout>
+      <div className="max-w-7xl mx-auto p-6">
+        <div className="space-y-6">
+          <div className="space-y-4">
+            <h1 className="text-3xl font-bold text-foreground">Graphs</h1>
+            <p className="text-muted-foreground text-lg">
+              Discover graph theory, algorithms on graphs, trees, and network analysis through interactive graph manipulation and visualization tools.
+            </p>
+          </div>
+
+          {/* Search bar */}
+          <div className="relative max-w-md">
+            <Search className="absolute left-3 top-1/2 transform -translate-y-1/2 text-muted-foreground w-4 h-4" />
+            <Input
+              placeholder="Search interactives..."
+              value={searchTerm}
+              onChange={e => setSearchTerm(e.target.value)}
+              className="pl-10"
+            />
+          </div>
+
+          {/* Gallery */}
+          <div className="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-3 gap-6">
+            {filteredInteractives.map(interactive => (
+              <Card
+                key={interactive.id}
+                className="cursor-pointer hover:shadow-lg transition-all duration-200 hover:scale-105"
+                onClick={() => setSelectedInteractive(interactive)}
+              >
+                <CardHeader className="space-y-3">
+                  <CardTitle className="text-xl text-foreground">{interactive.title}</CardTitle>
+                  <CardDescription className="text-muted-foreground line-clamp-3">
+                    {interactive.description}
+                  </CardDescription>
+                </CardHeader>
+                <CardContent>
+                  <div className="flex flex-wrap gap-2">
+                    {interactive.tags.map(tag => (
+                      <Badge key={tag} variant="secondary" className="text-xs">
+                        {tag}
+                      </Badge>
+                    ))}
+                  </div>
+                </CardContent>
+              </Card>
+            ))}
+          </div>
+
+          {filteredInteractives.length === 0 && (
+            <div className="text-center py-12">
+              <p className="text-muted-foreground text-lg">No interactives found matching your search.</p>
+            </div>
+          )}
+        </div>
+      </div>
+    </Layout>
   );
 };