Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 355 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 7 (d) 18
3. 3.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
5. 5.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 186 (c) 178 (d) 177
6. 6.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 192 (c) 183 (d) 193
7. 7.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 16 (c) 51 (d) 48
8. 8.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 531 (d) 532
9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 8 (d) 7
10. 10.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 201 (c) 202 (d) 192
11. 11.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 345 (c) 354 (d) 355
12. 12.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 53 (d) 62
13. 13.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
15. 15.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 5 (c) 45 (d) 15
16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 2 (c) 4 (d) 1
17. 17.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 283 (c) 273 (d) 282
18. 18.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 372 (c) 451 (d) 441
19. 19.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 322 (d) 321
20. 20.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 522 (c) 523 (d) 513
21. 21.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 118 (c) 109 (d) 110
22. 22.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 148 (c) 130 (d) 140
23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
24. 24.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
25. 25.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 111 (c) 120 (d) 102
26. 26.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 480 (c) 490 (d) 489
27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 15 (d) 16
28. 28.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 127 (c) 136 (d) 128
29. 29.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 180 (d) 190
30. 30.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
31. 31.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
32. 32.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 133 (c) 124 (d) 134
33. 33.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 24 (d) 72
34. 34.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 210 (c) 211 (d) 212
35. 35.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 12 (c) 36 (d) 108
36. 36.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 7 (c) 21 (d) 24
37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 171 (d) 57
38. 38.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 51 (c) 153 (d) 17
39. 39.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 481 (c) 480 (d) 471
40. 40.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 185 (c) 176 (d) 194

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