Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 822 · 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 13? (a) 14 (b) 7 (c) 5 (d) 6
2. 2.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
3. 3.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
4. 4.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 42 (d) 45
5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
6. 6.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
7. 7.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
8. 8.The numbers 9 to 17 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) 13 (c) 117 (d) 42
9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 17 (b) 18 (c) 16 (d) 6
10. 10.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 22 (c) 69 (d) 66
11. 11.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 33 (d) 36
12. 12.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 316 (c) 306 (d) 315
13. 13.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 166 (c) 184 (d) 175
14. 14.The numbers 14 to 22 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) 57 (c) 18 (d) 162
15. 15.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 135 (c) 15 (d) 45
16. 16.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 442 (c) 441 (d) 432
17. 17.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 258 (d) 270
18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 17 (d) 19
19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 3 (d) 5
20. 20.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) 9 (d) 30
21. 21.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
22. 22.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 333 (d) 334
23. 23.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 484 (c) 483 (d) 394
24. 24.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) 21 (b) 6 (c) 54 (d) 18
25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 18 (d) 16
26. 26.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 201 (c) 212 (d) 210
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
28. 28.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 216 (c) 24 (d) 72
29. 29.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 60 (d) 59
30. 30.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
31. 31.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
32. 32.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) 10 (b) 33 (c) 90 (d) 30
33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 18 (b) 7 (c) 17 (d) 19
34. 34.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
35. 35.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 86 (c) 77 (d) 68
36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 6 (c) 4 (d) 7
37. 37.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 630 (c) 498 (d) 640
38. 38.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 327 (c) 328 (d) 318
39. 39.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 366 (c) 357 (d) 367
40. 40.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 342 (c) 306 (d) 351

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