Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 797 · 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 5? (a) 5 (b) 6 (c) 4 (d) 10
2. 2.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 537 (c) 436 (d) 547
3. 3.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 50 (c) 49 (d) 40
4. 4.The numbers 5 to 13 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) 81 (c) 30 (d) 9
5. 5.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) 51 (c) 16 (d) 48
6. 6.The numbers 2 to 10 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) 21 (c) 18 (d) 6
7. 7.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 288 (c) 297 (d) 298
8. 8.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) 24 (d) 21
9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
10. 10.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
11. 11.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 288 (d) 324
12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 8 (b) 7 (c) 9 (d) 6
13. 13.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 194 (c) 186 (d) 176
14. 14.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 601 (b) 591 (c) 600 (d) 472
15. 15.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 125 (b) 126 (c) 116 (d) 134
16. 16.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) 17 (b) 54 (c) 153 (d) 51
17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
18. 18.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 304 (c) 274 (d) 294
19. 19.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 442 (b) 546 (c) 555 (d) 556
20. 20.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 519 (d) 520
21. 21.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 183 (c) 174 (d) 184
22. 22.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 460 (d) 583
23. 23.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 330 (c) 331 (d) 292
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
25. 25.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 258 (c) 249 (d) 259
26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
27. 27.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
28. 28.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 63? (a) 17 (b) 16 (c) 15 (d) 6
30. 30.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 276 (c) 297 (d) 307
31. 31.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 249 (c) 240 (d) 250
32. 32.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 368 (c) 444 (d) 435
33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 18 (d) 17
34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 8 (b) 20 (c) 18 (d) 19
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) 108 (b) 36 (c) 39 (d) 12
36. 36.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 118 (c) 117 (d) 126
37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 4 (c) 6 (d) 5
38. 38.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 10 (d) 30
39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 6 (b) 7 (c) 8 (d) 5
40. 40.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14

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