Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 5 · 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 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) 18 (b) 54 (c) 57 (d) 162
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
3. 3.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) 72 (b) 27 (c) 8 (d) 24
4. 4.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) 298 (c) 297 (d) 288
5. 5.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 260 (c) 283 (d) 282
6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 15 (b) 5 (c) 16 (d) 17
8. 8.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) 24 (b) 72 (c) 216 (d) 75
9. 9.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 120 (c) 119 (d) 128
10. 10.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 16 (b) 17 (c) 18 (d) 6
12. 12.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 163 (c) 172 (d) 164
13. 13.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 393 (d) 394
14. 14.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 84 (d) 83
15. 15.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) 90 (c) 30 (d) 33
16. 16.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 369 (c) 378 (d) 324
17. 17.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
18. 18.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
19. 19.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 80 (d) 79
20. 20.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 17 (d) 16
22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 7 (b) 10 (c) 5 (d) 9
23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
25. 25.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) 532 (d) 531
26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 5 (b) 6 (c) 4 (d) 3
27. 27.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 576 (c) 577 (d) 456
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 5 (b) 7 (c) 8 (d) 6
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 17 (c) 18 (d) 19
30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 19 (d) 17
31. 31.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) 60 (b) 180 (c) 63 (d) 20
32. 32.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) 15 (b) 48 (c) 45 (d) 135
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 18 (c) 6 (d) 17
34. 34.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 40 (c) 30 (d) 39
35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 16 (b) 7 (c) 17 (d) 18
36. 36.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) 171 (c) 60 (d) 57
37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 18 (b) 17 (c) 7 (d) 16
38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 16 (b) 15 (c) 5 (d) 17
39. 39.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 184 (c) 183 (d) 192
40. 40.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5

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