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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 96 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 9 (d) 19
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  4. 4.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) 57 (b) 171 (c) 60 (d) 19
  5. 5.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 50 (c) 68 (d) 60
  6. 6.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 20 (d) 21
  8. 8.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 173 (b) 182 (c) 164 (d) 174
  9. 9.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 640 (c) 630 (d) 639
  10. 10.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 13 (d) 8
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 7 (d) 4
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 3 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 19 (b) 9 (c) 18 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  20. 20.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
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 19 (d) 17
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 5 (b) 6 (c) 4 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 4 (d) 14
  26. 26.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 255 (c) 265 (d) 264
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 5 (d) 3
  30. 30.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 352 (c) 306 (d) 342
  31. 31.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 380 (c) 463 (d) 453
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
  33. 33.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) 22 (b) 69 (c) 198 (d) 66
  34. 34.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 445 (c) 368 (d) 444
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 14 (d) 13
  36. 36.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 403 (c) 393 (d) 340
  37. 37.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 438 (d) 429
  38. 38.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 390 (c) 332 (d) 391
  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) 63 (b) 7 (c) 24 (d) 21
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 5 (d) 15

Answer key

  1. 3
  2. 20
  3. 9
  4. 57
  5. 59
  6. 81
  7. 20
  8. 173
  9. 639
  10. 300
  11. 3
  12. 7
  13. 6
  14. 3
  15. 7
  16. 19
  17. 4
  18. 18
  19. 20
  20. 330
  21. 18
  22. 5
  23. 2
  24. 3
  25. 15
  26. 264
  27. 18
  28. 8
  29. 4
  30. 351
  31. 462
  32. 16
  33. 66
  34. 444
  35. 14
  36. 402
  37. 438
  38. 390
  39. 21
  40. 15

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