diff --git a/src/util/shards.ts b/src/util/shards.ts
new file mode 100644
index 0000000..87a1023
--- /dev/null
+++ b/src/util/shards.ts
@@ -0,0 +1,16 @@
+// Banana Split's fixed threshold policy: reconstruction requires a majority of
+// the shards, i.e. floor(total / 2) + 1. This lives in one place so the
+// generator (Share.vue) and the reprint view (Print.vue) can never disagree —
+// they did once: Print.vue re-implemented the formula as floor(total/2)+2 and
+// displayed the wrong "you need N more" count on reprints (finding F5).
+export function defaultThreshold(totalShards: number): number {
+  return Math.floor(totalShards / 2) + 1;
+}
+
+// Mirrors the min/max on the shard-count inputs. `v-model.number` on an
+// `<input type="number">` hands us whatever the field holds, which includes ""
+// for an empty box and fractions like 3.5 — neither is a shard count, so the
+// range check alone is not enough.
+export function isValidShardCount(value: unknown): value is number {
+  return typeof value === "number" && Number.isInteger(value) && value >= 3 && value <= 255;
+}
diff --git a/src/views/Print.vue b/src/views/Print.vue
index a207e74..624f637 100644
--- a/src/views/Print.vue
+++ b/src/views/Print.vue
@@ -11,10 +11,11 @@
             <br>
             <input
               id="totalShards"
-              v-model.number="requiredShards"
+              v-model.number="totalShards"
               type="number"
               min="3"
               max="255"
+              step="1"
             />
           </p>
           <button id="generateBtn" class="button-card" @click="handleShardsInput">
@@ -28,7 +29,7 @@
       <div v-if="numberEntered && needMoreShards">
         <qrcode-stream @decode="onDecode" />
       </div>
-      <div v-else-if="numberEntered">
+      <div v-else-if="numberEntered && threshold !== undefined">
         <button id="printBtn" class="button-card" @click="print">
           Print us!
         </button>
@@ -36,7 +37,7 @@
           v-for="code in qrCodes"
           :key="code"
           :shard="code"
-          :required-shards="parseInt(requiredShards/2)+2"
+          :required-shards="threshold"
           :title="title"
         />
       </div>
@@ -64,6 +65,7 @@
 
 <script lang="ts">
 import crypto, { Shard } from "../util/crypto";
+import { defaultThreshold, isValidShardCount } from "../util/shards";
 import ShardInfo from "../components/ShardInfo.vue";
 
 import Vue from "vue";
@@ -73,7 +75,7 @@ type PrintData = {
   nonce: string;
   shards: Shard[];
   qrCodes: Set<string>;
-  requiredShards?: number;
+  totalShards?: number;
   numberEntered: boolean;
   PLACEHOLDER_QR_DATA: string;
 };
@@ -87,21 +89,28 @@ export default Vue.extend({
       nonce: "",
       shards: [],
       qrCodes: new Set(),
-      requiredShards: undefined,
+      totalShards: undefined,
       numberEntered: false,
       PLACEHOLDER_QR_DATA: ""
     };
   },
   computed: {
     needMoreShards(): boolean {
-      return this.requiredShards !== undefined && this.shards.length !== this.requiredShards;
+      // Strictly "fewer than": scanning more codes than announced must not keep
+      // the scanner open (and must not make `remainingCodes` go negative).
+      return this.totalShards !== undefined && this.shards.length < this.totalShards;
     },
     remainingCodes(): number {
-      if (!this.requiredShards) {
+      if (!this.totalShards) {
         return 0;
       } else {
-        return this.requiredShards - this.shards.length;
+        return Math.max(0, this.totalShards - this.shards.length);
       }
+    },
+    // `undefined` until a valid count has been entered, so "not asked yet" stays
+    // distinguishable from a real threshold; the template guards on it.
+    threshold(): number | undefined {
+      return isValidShardCount(this.totalShards) ? defaultThreshold(this.totalShards) : undefined;
     }
   },
   mounted: function() {
@@ -144,10 +153,10 @@ export default Vue.extend({
       window.print();
     },
     handleShardsInput: function() {
-      if (this.requiredShards && this.requiredShards >= 3 && this.requiredShards <= 255) {
+      if (isValidShardCount(this.totalShards)) {
         this.numberEntered = true;
       } else {
-        this.$eventHub.$emit("showError", "Please enter a valid number of shards between 3 and 255.");
+        this.$eventHub.$emit("showError", "Please enter a whole number of shards between 3 and 255.");
       }
     },
     toggleMode: function() {
diff --git a/src/views/Share.vue b/src/views/Share.vue
index 24afd0f..f37b631 100644
--- a/src/views/Share.vue
+++ b/src/views/Share.vue
@@ -31,7 +31,7 @@
       <p>
         <label>3. Shards</label>
         <br />
-        Will require any {{ requiredShards }} shards out of
+        Will require any {{ requiredShardsLabel }} shards out of
         <input
           id="totalShards"
           v-model.number="totalShards"
@@ -39,13 +39,18 @@
           type="number"
           min="3"
           max="255"
+          step="1"
         />
         to reconstruct
+        <br />
+        <span v-if="!shardCountValid" class="error-text">
+          Enter a whole number of shards between 3 and 255
+        </span>
       </p>
       <button
         id="generateBtn"
         class="button-card"
-        :disabled="secretTooLong"
+        :disabled="secretTooLong || !shardCountValid"
         :hidden="encryptionMode"
         v-on:click="toggleMode"
       >
@@ -62,7 +67,7 @@
       </button>
     </div>
 
-    <div v-if="encryptionMode">
+    <div v-if="encryptionMode && requiredShards !== undefined">
       <div class="card" framed="true" transparent="true">
         <label>4. Your passphrase for the recovery is:</label>
         <div class="flex justify-between align-center">
@@ -91,6 +96,7 @@
 <script lang="ts">
 import passPhrase from "../util/passPhrase";
 import crypto from "../util/crypto";
+import { defaultThreshold, isValidShardCount } from "../util/shards";
 
 import ShardInfo from "../components/ShardInfo.vue";
 import CanvasText from "../components/CanvasText.vue";
@@ -120,12 +126,23 @@ export default Vue.extend({
     secretTooLong(): boolean {
       return this.secret.length > 1024;
     },
-    requiredShards(): number {
-      return Math.floor(this.totalShards / 2) + 1;
+    // Gates generation the same way `secretTooLong` does: a fractional or empty
+    // count would otherwise reach crypto.share() and fail deep inside secrets.js.
+    shardCountValid(): boolean {
+      return isValidShardCount(this.totalShards);
+    },
+    // Same contract as Print.vue's `threshold`: `undefined` while the count is
+    // not usable, so a coerced value ("" divides to 0, giving a bogus 1) can
+    // neither be printed nor reach ShardInfo's required Number prop.
+    requiredShards(): number | undefined {
+      return isValidShardCount(this.totalShards) ? defaultThreshold(this.totalShards) : undefined;
+    },
+    requiredShardsLabel(): string {
+      return this.requiredShards === undefined ? "—" : String(this.requiredShards);
     },
     shards(): string[] {
       this.$eventHub.$emit("clearAlerts");
-      if (!this.encryptionMode) {
+      if (!this.encryptionMode || this.requiredShards === undefined) {
         return [];
       }
       try {
diff --git a/tests/unit/shards.spec.ts b/tests/unit/shards.spec.ts
new file mode 100644
index 0000000..ea41d6b
--- /dev/null
+++ b/tests/unit/shards.spec.ts
@@ -0,0 +1,57 @@
+import { defaultThreshold, isValidShardCount } from "../../src/util/shards";
+
+describe("defaultThreshold", () => {
+  // The bug fixed in F5 was Print.vue computing floor(total/2)+2 instead of
+  // floor(total/2)+1 — e.g. total=5 showed "need 4" instead of the correct 3.
+  test.each([
+    [3, 2],
+    [4, 3],
+    [5, 3], // the exact case from finding F5
+    [6, 4],
+    [7, 4],
+    [10, 6],
+    [19, 10],
+    [255, 128]
+  ])("threshold for %i total shards is %i", (total, expected) => {
+    expect(defaultThreshold(total)).toBe(expected);
+  });
+
+  // A lower bound alone is too weak to pin the policy: floor(8/2)+2 = 6 is also
+  // "more than half of 8". Assert the threshold is the *smallest* strict
+  // majority, which is the property that makes floor(n/2)+1 the only answer.
+  test("is the smallest strict majority across the whole UI range", () => {
+    for (let n = 3; n <= 255; n++) {
+      const threshold = defaultThreshold(n);
+      expect(threshold).toBeGreaterThan(n / 2);
+      expect(threshold - 1).toBeLessThanOrEqual(n / 2);
+    }
+  });
+});
+
+describe("isValidShardCount", () => {
+  test("accepts every whole number the UI offers", () => {
+    for (let n = 3; n <= 255; n++) {
+      expect(isValidShardCount(n)).toBe(true);
+    }
+  });
+
+  // Annotated as unknown[][] on purpose: these are the values the input can
+  // actually hand us, not just out-of-range numbers.
+  const rejected: unknown[][] = [
+    [2, "below the minimum"],
+    [256, "above the maximum"],
+    [0, "zero"],
+    [-5, "negative"],
+    [3.5, "fractional — type=number accepts it, step=1 only nudges the spinner"],
+    [Number.NaN, "NaN"],
+    [Number.POSITIVE_INFINITY, "infinite"],
+    ["", "an emptied input, which v-model.number leaves as a string"],
+    ["5", "a numeric string"],
+    [undefined, "the initial data value"],
+    [null, "null"]
+  ];
+
+  test.each(rejected)("rejects %p (%s)", value => {
+    expect(isValidShardCount(value)).toBe(false);
+  });
+});