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IMO 1960 Problem 01

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license : MIT License
modified : 2009/07/07 22:27:12

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<?xml version="1.0" encoding="utf-8"?>
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml" layout="absolute"
                width="480" height="360" backgroundColor="#FFFFFF" xmlns="*">

<mx:ApplicationControlBar dock="true" width="100%">
        <mx:Label id="lblProblem" x="10" y="10" width="380" height="80">
            <mx:text>
            <![CDATA[
         IMO 1960 Problem 01
         Determine all three-digit numbers N having the property
         that N is divisible by 11, and N/11 is equal to the sum of
         the squares of the digits of N.
            ]]>
            </mx:text>
        </mx:Label>
        <mx:Button id="btnSolve" x="395" y="55" click="solve();" label="Solve!" />
    </mx:ApplicationControlBar>
    <mx:Script>
        <![CDATA[
            public function solve():void {
                txtResult.text = "";
                var count:int = 1;

var k:int = 10;
                while (k * 11 < 1000) {
                    // Calculate sum of the squares of the digits
                    var sumSquares:int = 0;
                    var n:int = k * 11;
                    while (n > 0) {
                        var digit:int = n % 10;
                        sumSquares += digit * digit;
                        n /= 10;
                    }

// Check
                    if (sumSquares == k) {
                        txtResult.text += count + ") " + (k * 11) + "\n";
                        ++count;
                    }
                    ++k;
                }
            }
        ]]>
    </mx:Script>
    <mx:TextArea id="txtResult" x="5" y="15" width="470" height="250" />

</mx:Application>

math problem

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IMO 1960 Problem 01 IMO 1962 Problem 01 [diff(29)]

_ex_

<?xml version="1.0" encoding="utf-8"?>
<mx:Application xmlns:mx="http://www.adobe.com/2006/mxml" layout="absolute"
width="480" height="360" backgroundColor="#FFFFFF" xmlns="*">
<mx:ApplicationControlBar dock="true" width="100%">
<mx:Label id="lblProblem" x="10" y="10" width="380" height="140">
<mx:text>
<![CDATA[
IMO 1962 Problem 01
Find the smallest natural number n which has the following
properties:
(a) Its decimal representation has 6 as the last digit.
(b) If the last digit 6 is erased and placed in front of
the remaining digits, the resulting number is four
times as large as the original number n.
]]>
</mx:text>
</mx:Label>
<mx:Button id="btnSolve" x="395" y="115" click="solve();" label="Solve!" />
</mx:ApplicationControlBar>
<mx:Script>
<![CDATA[
public function solve():void {
txtResult.text = "";
var k:int = 1;
var k_up:int = 10; // Minimum (10^p) greater that k.
while (true) {
var n:int = (10 * k) + 6;
var m:int = (6 * k_up) + k;
// Check
if (m == 4 * n) {
txtResult.text += "ANSWER: " + n;
break;
}
++k;
if (k >= k_up) {
k_up *= 10;
}
}
}
]]>
</mx:Script>
<mx:TextArea id="txtResult" x="5" y="15" width="470" height="190" />
</mx:Application>