答案:30
推理分析:
(一)张三:我不知道这个数是多少,但是保证你们也不知道;
也就是说个位数和十位数的和不唯一。
如果我们将所有两位数按数字之和分组的话,那么只有组中元素个数>1时,才满足条件。
按数字之和分组:
1: [10],
2: [11, 20],
3: [12, 21, 30],
4: [13, 22, 31, 40],
5: [14, 23, 32, 41, 50],
6: [15, 24, 33, 42, 51, 60],
7: [16, 25, 34, 43, 52, 61, 70],
8: [17, 26, 35, 44, 53, 62, 71, 80],
9: [18, 27, 36, 45, 54, 63, 72, 81, 90],
10: [19, 28, 37, 46, 55, 64, 73, 82, 91],
11: [29, 38, 47, 56, 65, 74, 83, 92],
12: [39, 48, 57, 66, 75, 84, 93],
13: [49, 58, 67, 76, 85, 94],
14: [59, 68, 77, 86, 95],
15: [69, 78, 87, 96],
16: [79, 88, 97],
17: [89, 98],
18: [99]
筛选后:
2: [11, 20],
3: [12, 21, 30],
4: [13, 22, 31, 40],
5: [14, 23, 32, 41, 50],
6: [15, 24, 33, 42, 51, 60],
7: [16, 25, 34, 43, 52, 61, 70],
8: [17, 26, 35, 44, 53, 62, 71, 80],
9: [18, 27, 36, 45, 54, 63, 72, 81, 90],
10: [19, 28, 37, 46, 55, 64, 73, 82, 91],
11: [29, 38, 47, 56, 65, 74, 83, 92],
12: [39, 48, 57, 66, 75, 84, 93],
13: [49, 58, 67, 76, 85, 94],
14: [59, 68, 77, 86, 95],
15: [69, 78, 87, 96],
16: [79, 88, 97],
17: [89, 98]
(二)李四:我确实不知道,但是知道这个数的奇偶性;
也就是说如果我们将上述两位数按约数个数分组,只有组中元素同为奇数或者偶数,并且元素个数>1的分组才满足条件。
按约数个数分组:
2: [11, 13, 31, 23, 41, 43, 61, 17, 53, 71, 19, 37, 73, 29, 47, 83, 67, 59, 79, 97, 89],
3: [25, 49],
4: [21, 22, 14, 15, 33, 51, 34, 26, 35, 62, 27, 46, 55, 82, 91, 38, 65, 74, 39, 57, 93, 58, 85, 94, 77, 86, 95, 69, 87],
5: [16, 81],
6: [20, 12, 32, 50, 52, 44, 18, 45, 63, 28, 92, 75, 76, 68, 98],
7: [64],
8: [30, 40, 24, 42, 70, 54, 56, 66, 78, 88],
9: [36],
10: [80, 48],
12: [60, 72, 90, 84, 96]
筛选后:
2: [11, 13, 31, 23, 41, 43, 61, 17, 53, 71, 19, 37, 73, 29, 47, 83, 67, 59, 79, 97, 89],
3: [25, 49],
8: [30, 40, 24, 42, 70, 54, 56, 66, 78, 88],
10: [80, 48],
12: [60, 72, 90, 84, 96]
(三)张三:听了你这么说,我现在知道了;
也就是如果我们将上述两位数按数字之和分组的话,那么只有组中元素只有一个时,才满足条件。
按数字之和分组:
2: [11],
3: [30],
4: [40, 13, 31],
5: [23, 41],
6: [24, 42, 60],
7: [70, 43, 61, 25],
8: [17, 53, 71, 80],
9: [54, 72, 90],
10: [19, 37, 73],
11: [56, 29, 47, 83],
12: [66, 84, 48],
13: [67, 49],
14: [59],
15: [78, 96],
16: [88, 79, 97],
17: [89]
筛选后:
2: [11],
3: [30],
14: [59],
17: [89]
(四)王五:我也知道了;
也就是说,上面四个数中有一个数的约数个数是独特的,可以排除另外3个数。
11、59、89都是有2个约数,只有30不是两个约数。
(五)李四:我也知道了。
同样,李四也能排除确定这个数是30。
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