Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 945 · 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.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) 30 (d) 10
2. 2.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
4. 4.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 72 (c) 54 (d) 63
5. 5.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
6. 6.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 366 (c) 316 (d) 367
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 17 (d) 16
8. 8.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 20 (d) 60
9. 9.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 276 (c) 285 (d) 262
10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 16 (b) 4 (c) 14 (d) 15
11. 11.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 607 (c) 606 (d) 476
12. 12.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) 21 (b) 24 (c) 7 (d) 63
13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 4 (d) 3
14. 14.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 405 (c) 406 (d) 396
15. 15.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) 69 (c) 66 (d) 22
16. 16.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) 16 (b) 144 (c) 51 (d) 48
17. 17.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
18. 18.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 3 (b) 15 (c) 13 (d) 14
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) 9 (b) 30 (c) 27 (d) 81
21. 21.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 137 (c) 146 (d) 138
22. 22.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) 45 (d) 42
23. 23.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 603 (c) 612 (d) 480
24. 24.The numbers 17 to 25 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) 66 (c) 21 (d) 189
25. 25.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 225 (c) 228 (d) 234
26. 26.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 456 (c) 382 (d) 466
27. 27.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
28. 28.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) 153 (b) 51 (c) 17 (d) 54
29. 29.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 246 (c) 255 (d) 256
30. 30.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) 117 (b) 42 (c) 13 (d) 39
31. 31.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 174 (d) 184
32. 32.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) 72 (c) 24 (d) 8
33. 33.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 13 (c) 4 (d) 14
35. 35.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
36. 36.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) 5 (b) 18 (c) 45 (d) 15
37. 37.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 522 (c) 420 (d) 523
38. 38.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 126 (c) 118 (d) 108
39. 39.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) 292 (d) 331
40. 40.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 364 (c) 439 (d) 438

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