```ts
export function applyCharges(caps: Record<string, [number, number]>, charges: [string, string, number][]): { left: Record<string, number>; refused: [string, string][] } {
    const result: { left: Record<string, number>; refused: [string, string][] } = { left: {}, refused: [] };

    for (const charge of charges) {
        const [chargeId, bucketName, amount] = charge;

        if (!caps[bucketName]) {
            result.refused.push([chargeId, 'unknown']);
            continue;
        }

        if (amount <= 0 || !Number.isInteger(amount)) {
            throw new Error('Amount must be a positive whole number');
        }

        const [allowance, maxSingleCharge] = caps[bucketName];

        if (amount > maxSingleCharge) {
            result.refused.push([chargeId, 'single']);
            continue;
        }

        if (amount > allowance) {
            result.refused.push([chargeId, 'cap']);
            continue;
        }

        if (!result.left[bucketName]) {
            result.left[bucketName] = allowance - amount;
        } else {
            result.left[bucketName] -= amount;
        }
    }

    return result;
}
```