Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 392 · 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.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 236 (b) 246 (c) 237 (d) 247
2. 2.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) 18 (b) 21 (c) 6 (d) 54
3. 3.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) 36 (b) 99 (c) 11 (d) 33
4. 4.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
5. 5.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) 20 (c) 63 (d) 60
6. 6.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) 8 (b) 72 (c) 24 (d) 27
7. 7.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 441 (c) 442 (d) 366
8. 8.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) 15 (d) 45
9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 3 (d) 1
10. 10.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
11. 11.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 338 (d) 399
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 16 (d) 17
13. 13.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
14. 14.The numbers 19 to 27 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) 69 (c) 207 (d) 23
15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 16 (b) 14 (c) 15 (d) 4
16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 20 (d) 9
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 15 (b) 14 (c) 5 (d) 16
18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 16 (b) 18 (c) 17 (d) 7
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 3 (b) 6 (c) 5 (d) 4
21. 21.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) 27 (c) 81 (d) 30
22. 22.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 2 (c) 10 (d) 4
23. 23.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 393 (c) 403 (d) 402
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 18 (d) 17
25. 25.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
26. 26.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 292 (c) 291 (d) 266
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 4 (c) 16 (d) 15
28. 28.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 4 (c) 2 (d) 5
30. 30.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 315 (c) 306 (d) 282
31. 31.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
32. 32.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) 21 (b) 66 (c) 63 (d) 189
33. 33.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 114 (d) 132
34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 5 (d) 4
35. 35.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 601 (c) 600 (d) 591
36. 36.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) 57 (b) 162 (c) 54 (d) 18
37. 37.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 7 (b) 5 (c) 4 (d) 6
39. 39.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) 24 (b) 21 (c) 63 (d) 7
40. 40.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) 60 (b) 19 (c) 171 (d) 57

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