[Answer] Mathematics × Programming Competition #8 - Four Digit Calculator

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Math and Programming Competition

Given a four digit calculator, if you rotate it by 180 degree, you may get another ‘valid’ number. For example,

0159

0159 becomes 6510 if rotated 180 degree. The ‘1’ is still valid even it is on the other side.

6510

The question comes: how many numbers are required to represent from 0000 to 9999?

First, we need a function to tell if a digit can be rotated… if not, e.g. like 7, we need to return false.

function getRevDig(x) {
    switch (x) {
        case 0: return 0;
        case 1: return 1;
        case 2: return 2;
        case 5: return 5;
        case 6: return 9;
        case 8: return 8;
        case 9: return 6;
        default: return false;
    }
}

function getRevDig(x) {
    switch (x) {
        case 0: return 0;
        case 1: return 1;
        case 2: return 2;
        case 5: return 5;
        case 6: return 9;
        case 8: return 8;
        case 9: return 6;
        default: return false;
    }
}

Now, given a four digit number, we need to return its rotated version, to get each digit, you can use module operator and division.

function getRev(x) {
    var a = x % 10;
    a = getRevDig(a);
    if (a === false) return false;
    var b = Math.floor(x / 10) % 10;
    b = getRevDig(b);
    if (b === false) return false;
    var c = Math.floor(x / 100) % 10;
    c = getRevDig(c);
    if (c === false) return false;  
    var d = Math.floor(x / 1000);
    d = getRevDig(d);
    if (d === false) return false;  
    return (a * 1000 + b * 100 + c * 10 + d);
}

function getRev(x) {
    var a = x % 10;
    a = getRevDig(a);
    if (a === false) return false;
    var b = Math.floor(x / 10) % 10;
    b = getRevDig(b);
    if (b === false) return false;
    var c = Math.floor(x / 100) % 10;
    c = getRevDig(c);
    if (c === false) return false;  
    var d = Math.floor(x / 1000);
    d = getRevDig(d);
    if (d === false) return false;  
    return (a * 1000 + b * 100 + c * 10 + d);
}

The rest is straightforward, just to check and mark the number and its flipped version in a dictionary-like data structure (or array).

var total = 0;
var a = {};
for (var i = 0; i <= 9999; ++i) {
    if (!(i in a)) {
        total ++;
        a[i] = 1;
        var x = getRev(i);
        if (x !== false) {
            a[x] = 1;
        }
    }
}
console.log(total);

var total = 0;
var a = {};
for (var i = 0; i <= 9999; ++i) {
    if (!(i in a)) {
        total ++;
        a[i] = 1;
        var x = getRev(i);
        if (x !== false) {
            a[x] = 1;
        }
    }
}
console.log(total);

That should give you the correct answer – 8824.

–EOF (The Ultimate Computing & Technology Blog) —

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