Find the points where "0.67*x" and "2/3*x" round to the same number to two decimal places, but "0.66*x" rounds to something else.

rounding-two-thirds-x.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def p(x):\n",
    "    # return true if 0.67*x and 2/3*x agree to two decimal places, but 0.66*x is something else\n",
    "    a,b,c = ('{0:.2f}'.format(x) for x in (0.67*x,2/3*x,0.66*x))\n",
    "    return a==b and b!=c "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4d82c30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(15,2))\n",
    "ax.get_yaxis().set_visible(False)\n",
    "n = 10000\n",
    "a,b = 0.99,1.01\n",
    "xs = [x for x in [(b-a)*x/n+a for x in range(0,n) ] if p(x)]\n",
    "ys = [1]*len(xs)\n",
    "scale = 1\n",
    "ax.scatter(xs, ys, s=3, alpha=0.3, edgecolors='none')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "!\t0.9901062107116154\t0.66 0.66 0.65\n",
      "!\t0.9902250528576588\t0.66 0.66 0.65\n",
      "!\t0.9921171875953435\t0.66 0.66 0.65\n",
      "!\t0.9922815901840906\t0.66 0.66 0.65\n",
      " \t0.9927286010078373\t0.67 0.66 0.66\n",
      " \t0.9928939794367649\t0.67 0.66 0.66\n",
      " \t0.9932649410400956\t0.67 0.66 0.66\n",
      " \t0.9932761604262923\t0.67 0.66 0.66\n",
      " \t0.9932876920090452\t0.67 0.66 0.66\n",
      " \t0.9937114766215758\t0.67 0.66 0.66\n",
      " \t0.9940599540959716\t0.67 0.66 0.66\n",
      " \t0.9942284568151343\t0.67 0.66 0.66\n",
      " \t0.9943239672938083\t0.67 0.66 0.66\n",
      " \t0.9950924073921029\t0.67 0.66 0.66\n",
      " \t0.9955175363390599\t0.67 0.66 0.66\n",
      " \t0.9955865260534439\t0.67 0.66 0.66\n",
      " \t0.9963359706603602\t0.67 0.66 0.66\n",
      " \t0.9963559785252695\t0.67 0.66 0.66\n",
      " \t0.9970240590848033\t0.67 0.66 0.66\n",
      " \t0.9971207139644296\t0.67 0.66 0.66\n",
      " \t0.9972273506871502\t0.67 0.66 0.66\n",
      " \t0.9973565046248328\t0.67 0.66 0.66\n",
      " \t0.9974421300307009\t0.67 0.66 0.66\n",
      "!\t0.9978831886852849\t0.67 0.67 0.66\n",
      "!\t0.997984310277999\t0.67 0.67 0.66\n",
      "!\t0.998112630715233\t0.67 0.67 0.66\n",
      "!\t0.9987364532763212\t0.67 0.67 0.66\n",
      "!\t0.9998168768844163\t0.67 0.67 0.66\n",
      "!\t0.9998773948351627\t0.67 0.67 0.66\n",
      "!\t0.9999932278336782\t0.67 0.67 0.66\n",
      "!\t1.0000340580783924\t0.67 0.67 0.66\n",
      "!\t1.0001875354527374\t0.67 0.67 0.66\n",
      "!\t1.0005713130813718\t0.67 0.67 0.66\n",
      "!\t1.0008307809690682\t0.67 0.67 0.66\n",
      "!\t1.0011398036620764\t0.67 0.67 0.66\n",
      "!\t1.0012416307811904\t0.67 0.67 0.66\n",
      "!\t1.0016001488337687\t0.67 0.67 0.66\n",
      "!\t1.0019658079764182\t0.67 0.67 0.66\n",
      "!\t1.0026370427137192\t0.67 0.67 0.66\n",
      "!\t1.002922822783715\t0.67 0.67 0.66\n",
      "!\t1.0032375320806453\t0.67 0.67 0.66\n",
      "!\t1.004058759281178\t0.67 0.67 0.66\n",
      "!\t1.0041101107969819\t0.67 0.67 0.66\n",
      "!\t1.0049996600704119\t0.67 0.67 0.66\n",
      "!\t1.005791398684193\t0.67 0.67 0.66\n",
      "!\t1.0060714805739277\t0.67 0.67 0.66\n",
      "!\t1.0064446570908008\t0.67 0.67 0.66\n",
      " \t1.0077372827203597\t0.68 0.67 0.67\n",
      " \t1.0085120539418937\t0.68 0.67 0.67\n",
      " \t1.009873098014959\t0.68 0.67 0.67\n"
     ]
    }
   ],
   "source": [
    "from random import random\n",
    "xs = [(b-a)*random()+a for x in range(50)]\n",
    "xs.sort()\n",
    "print('\\n'.join(['{}\\t{}\\t{}'.format('!' if p(x) else ' ', x,' '.join('{0:.2f}'.format(x) for x in (0.67*x,2/3*x,0.66*x))) for x in xs]))"
   ]
  }
 ],
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