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2017
小學數學競賽選拔賽初賽試題
第 一 試：計 算 題 (考試時間 1 小時)
◎
請將答案填入答案卷對應題號的空格內，不須計算過程。答案若為分數請化
為最簡分數。本題目卷正反面空白處可為作演算草稿紙。每題 5 分，共 100 分
1.
2017
2017
2017
2017
2017
+
+
+
+
=
？
2017 5
(2000 17) 5
2000 5 17 5 10000 85 10085
=
× =
+
× =
× + × =
+
=
2.
1000000
2
2
2 2
2 5 5 5 5
÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ =
？
【參考解法
1
】
2 2 2 2 2 2 5 5 5 5 5 5 2 2 2 2 2 5 5 5 5
2 5 5
50
= × × × × × × × × × × × ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷
= × × =
【參考解法 2】
1000000 10000 2 100 2
50
=
÷
÷ =
÷ =
3.
222222222
22222222
2222222
222222 11111 1111 111 11 1
+
+
+
−
−
−
− − =
？
(222222222
22222222
2222222
222222) (11111 1111 111 11 1)
246888888 12345
246876543
=
+
+
+
−
+
+
+ +
=
−
=
4.
240 70 80 350 60 420
÷
÷ ×
÷ ×
=
？
240 80 350 70 420 60
3 5 7 105
=
÷ ×
÷ ×
÷
= × × =
5.
24 60 60
× ×
=
？
【參考解法 1】
24 36 100
(30 6) (30 6) 100
(30 30 6 6) 100
(900 36) 100
86400
=
× ×
=
− ×
+ ×
=
× − × ×
=
−
×
=
【參考解法 2】
24 6 6 100
144 6 100
86400
=
× × ×
=
× ×
=
6.
20.27
(60.71 40.73)
80.16
(179.79 100.84)
−
−
+
−
−
=
？
【參考解法 1】
20.27 60.71 40.73 80.16 179.79 100.84
(20.27
40.73) 60.71 (80.16 100.84) 179.79
61 60.71 181 179.79
0.29 1.21 1.5
=
−
+
+
−
+
=
+
−
+
+
−
=
−
+
−
=
+
=
【參考解法
2
】
20.27 60.71 40.73 80.16 179.79 100.84
(20 60 40 80 179 100)
(0.27 0.71 0.73 0.16 0.79 0.84)
1 (2 1.5)
1.5
=
−
+
+
−
+
=
−
+
+
−
+
+
−
+
+
−
+
= + −
=
7.
71.02 10.27
2.71 27.1
+
+
+
=
？
(71 10 2
27)
(0.2 0.27 0.71 0.1)
110 1.1=111.1
=
+ + +
+
+
+
+
=
+
8.
4.3
6.18
2.02
(
) 99
12.9
12.36
12.12
+
−
×
=
？
1
1
1
5
1
4
2
(
) 99
(
) 99
99
99
66
3
2
6
6
6
6
3
=
+ − ×
=
− ×
= ×
= ×
=
9.
7 13 19
25
1999
2005
2011 2017
+ + +
+ +
+
+
+
=
⋯
？
168
(7
2017)
(13 2011)
(19
2005)
(25 1999)
(1009 1015)
2024
2024
2024
2024
2024 168
340032
= +
+
+
+
+
+
+
+ +
+
=
+
+
+ +
=
×
=
⋯
⋯
項
10.
20 17
40 34
60 51 80 68 100 85 120 102 140 119 160 136
− +
−
+
− +
−
+
−
+
−
+
−
+
−
=
？
【參考解法 1】
(20 17)
(40 34)
(60 51)
(80
68)
(100 85)
(120 102)
(140 119)
(160 136)
(3
24) 8
3 6
9 12 15 18
21 24
108
2
=
−
+
−
+
−
+
−
+
−
+
−
+
−
+
−
+
×
= + + + + + +
+
=
=
【參考解法
2
】
(20 40 60 80 100 120 140 160) (17 34 51 68 85 102 119 136)
(20 160) 8
(17 136) 8
(180 153) 4
27 4
108
2
2
=
+
+
+
+
+
+
+
−
+
+ +
+ +
+
+
+
×
+
×
=
−
=
−
× =
× =
11.
(22001177
22110077 112277
221177 11002277 11220077)
6
+
+
+
+
+
÷ =
？
((22001100 22110000 112200 221100 11002200 11220000)
77 6) 6
66666600 6 77 11111100 77
11111177
=
+
+
+
+
+
+
× ÷
=
÷ +
=
+
=
12.
5000
2048 1024 512
256 128 64 32 16 8
4
2 1
−
−
−
−
−
−
−
− − − − − =
？
5000 (1 2
4 8 16 32 64 128 256 512 1024
2048)
2048 2 1
5000 (
)
5000 4095
905
2 1
=
− + + + + +
+
+
+
+
+
+
× −
=
−
=
−
=
−
13.
128
2
2017
63
63
×
−
=
？
2
2
2
2
2
2017 (2
)
4034
2017
4034
2016
4034
64
4098
63
63
63
63
63
=
× +
−
=
+
×
−
=
+
×
=
+
=
14.
3
1
17
1
3
1
41
0.25
41.15
18
41
41.15
20
3
20
6
20
4
×
+
× +
+ ×
+
× =
？
3
1
3
1
17
1
3
3
1
41
41
18
41
41
20
4
20
3
20
6
20
20
4
3
1
1
1
1
17
3
17
41
(
) 18
41
1 18
60
20
4
3
6
4
20
20
20
=
× +
× +
+ ×
+
×
=
×
+ + +
+
=
× +
=
15.
999
999 999
999 999 999
+
×
+
×
×
=
？
【參考解法 1】
999 (1 999)
999 999 999
999 1000 999 999 999
999 (1000 999 999)
(1000 1) (1000 (1000 1) (1000 1))
(1000 1) (1000 1000000 2000 1)
(1000 1) 999001
999001000 999001 998001999
=
× +
+
×
×
=
×
+
×
×
=
×
+
×
=
− ×
+
− ×
−
=
− ×
+
−
+ =
− ×
=
−
=
【參考解法
2
】
999 999 999 (1 999)
999 999 999 1000
999 (1 999000)
999 999 999000
999 (1000 1) (1000000 1000)
999 1000000000 1000000 1000000 1000
1000001999 2000000
998001999
=
+
×
× +
=
+
×
×
=
× +
=
+
×
=
+
− ×
−
=
+
−
−
+
=
−
=
16.
460
297
598
37
91
1
1
9
243
77
(
)
2
6
10
÷
÷
=
÷
− +
？
460
297
598
460
91
1
37
243
37
91
37
243
37
297
77
30
598
77
30
46 10
7 13
1
37
9 27
1
1
3
3
37
11 27
7 11 3 10
46 13
11 11
121
÷
=
÷
=
×
×
×
×
÷
×
×
×
=
×
×
×
×
=
× × =
×
×
×
×
17.
154154
49 1573
462462 121 637
÷
÷
+
÷
÷
=
？
【參考解法
1
】
1
1
1
1
154154
154154 3
49 1573
121 637
1
1
1
1
154154
(
3
)
49 121
13
13
1
1
4
154 1001
7 7 11 11 13
1
1
1
1
154
4
11 14
4
8
7 11
7 11
=
×
×
+
× ×
×
=
×
×
×
+ ×
=
×
×
×
×
×
×
=
× × × = × × × × =
【參考解法
2
】
1
1
1
1
154154
154154 3
49 1573
121 637
1
1
154154
154154 3
77077
77077
1
154154 4
2 4
8
77077
=
×
×
+
× ×
×
=
×
+
× ×
=
× ×
= × =
18.
(41590 8193 20170)
(4158 819.4
201.8)
×
−
÷
×
+
=
？
10 (4159 8193 2017) (0.1 (4158 8194
2018))
100 (4159 8193 2017) ((4159 1) (8193 1)
2018)
100 (4159 8193 2017) (4159 8193 1 8193 4159 1 1 1 2018)
100 (4159 8193 2017) (4159 8193 8193 4159 1 2018)
100
= ×
×
−
÷
×
×
+
=
×
×
−
÷
− ×
+ +
=
×
×
−
÷
×
− ×
+
× − × +
=
×
×
−
÷
×
−
+
− +
=
×
(4159 8193 2017) (4159 8193 2017)
100
×
−
÷
×
−
=
19.
7
37
85
148
235
337
10
40
88
151
238
340
+
+
+
+
+
=
？
3
3
3
3
3
3
(1
)
(1
)
(1
)
(1
)
(1
)
(1
)
10
40
88
151
238
340
3
3
3
3
3
3
(
)
10
40
88
151
238
340
3
3
3
3
3
3
(
)
2 5
5 8
8 11
11 14
14 17
17 20
1
1
1
1
1
1
1
1
1
1
1
1
(
)
2
5
5
8
8
11 11 14
14
17
17
20
1
1
9
11
1
(
)
.55
6
6
6
2
20
2
6
6
5
0
20
5
= −
+ −
+ −
+ −
+ −
+ −
= −
+
+
+
+
+
= −
+
+
+
+
+
×
×
×
×
×
×
= −
− + − + −
+
−
+
−
+
−
= −
−
= −
=
=
=
1
1
20
20.
1
1
1
512
511
510
1
1
1
1
1
1
1
(1
)(1
)
(1
)(1
)(1
)
512
512
511
512
511
510
+
+
+
+
+
+
+
+
+
⋯⋯
1
456
1
1
1
1
(1
)(1
)(1
)
(1
)
512
511
510
456
+
=
+
+
+
+
⋯
？
57
1
1
1
1
512
511
510
456
513
513
512
513
512
511
513
512
511
457
512
512
511
512
511
510
512
511
510
456
1
1
1
1
513
513
513
513
1
1
=
57=
513
9
=
+
+
+ +
×
×
×
×
×
× ×
=
+
+
+ +
×
⋯
⋯
⋯
項