Download 5th Math Week 4: Cryptarithms and more Study notes Calculus in PDF only on Docsity! 5th Math Week 4: Cryptarithms A Cryptarithm is a mathematical puzzle where the digits in a sum have been replaced by letters. • In each of the puzzles below, each letter stands for a different digit • 0 is never the first digit of any number. Can you find a solution to all of these cryptarithms? Do any of them have more than one solution? Do any of them have more than one solution? How can you be sure that you have found all the solutions to each cryptarithm? Source: http://nrich.maths.org/11107 Week 4: Notes & Solutions Notes & Hints • Try to think about the biggest or smallest numbers you could add together in each case. • Does that tell you anything about the digits of the number that they sum to ? • If you add two 2 digit numbers together to make a 3 digit number, what could the first digit of that number be? Solution Here is a list of all the solutions we have managed to find for each puzzle. Please let us know if you discover any more! 1) A=5,B=1. 2) A=1,B=9,C=0. 3) A=9,B=1,C=0. 4) A=9,B=2,C=1,D=0. 5) A=9,B=1,C=0. 6) A=2,B=6,C=3 or A=4,B=7,C=2 or A=6,B=8,C=1. 7) A=2,B=1,C=9. 8) A=2,B=3,C=9. 9) A=9,B=2,C=1. 10) A=5,B=0,C=1. 11) A=2,B=1,C=4 or A=2,B=6,C=5 or A=4,B=2,C=8 or A=4,B=7,C=9. 12) A=1,B=2,C=4 or A=2,B=4,C=8 or A=2,B=5,C=0 or A=3,B=7,C=4 or A=4,13)B=9,C=8. 13) A=5,B=9,C=6. 14) A=4,B=5,C=9. 15) A=7,B=2,C=1. 16) A=9,B=2,C=1,D=0,E=4. 17) A=1,B=8,C=5. 18) A=1,B=4,C=8. 19) A=1,B=9,C=8. 20) A=4,B=7,C=6. 21) A=2,B=9,C=8. 22) A=9,B=4,C=1,D=6. 23) A=5,B=7,2,D=8. Explanation of #1 A+A+A=BA. A+A+A must equal a number above 10 because it equals a two digit number (BA). Then you must work out which three numbers under 10 are added together to equal a number under 30 with the same second digit. A also has to be 4 or above because 3×3=9 which is not a two digit number. Then try trial and error with this information 4+4+4=12 5+5+5=15 6+6+6=18 7+7+7=21 8+8+8=24 9+9+9=27 By doing this you will be able to find out your answer. A=5 B=1 Several people worked out that for the next few problems, the first digit of the total would be 1. MJ from the Bourne Academy explained it like this:
