# Crunching numbers with Vikram and Betaal

Anil Kumar Patnaik

The undaunted king, Vikram, marched to the gnarled banyan tree with his sword. He cut the ropes that tied the corpse to the tree, lifted the body that fell down on to his shoulders and started walking back. Betaal said, “Hey King Vikram! The way is humdrum. Let me tell you the tale of a mathematics teacher to keep you amused.”

Betaal started – Abhas was an inspiring, enthusiastic mathematics teacher, very popular, because of his communication and presentation skills. One day, due to rains, the games period of a particular class got cancelled and Abhas was called in as the substitute teacher. As he entered the class, the students shouted in chorus, “We want games…, we want games…,” to which Abhas replied, “Yes, of course… but inside the classroom, we will have math games with numbers. Give me a five digit number, and before calculating I will tell you the answer to a five-step addition.” This sounded interesting to the students and they were quiet now. He called Prakriti, a skilled scholar of the class, and asked her to write a five digit number on the board. Prakriti wrote 56287. Abhas wrote something on a paper and kept it on the table. (He had written the number 256285). He then called upon Falak to write a number; she wrote 79286. Abhas wrote 20713 on the blackboard. Next Joseph wrote 35941. Abhas wrote 64058. Then, he said, “Prakriti, you are good at addition. Please come and let us know the total.” Prakriti wrote the numbers in a column and added them, the result was 256285. Now he said, “Okay, open the paper and show.” The children were taken aback…. “Woww…uuu… how did you do that! please tell us…,” a group of students requested. He just smiled and kept quiet.

Elen, a polymath of the class asked, “Sir, these are five digit numbers, can you do the same for seven digit numbers with more steps?” “Yes,” Abhas replied. “Please come and write a seven digit number. Elen wrote 5726841. This time Abhas wrote a number on the paper and kept it on the table (the number he had written was 35726838). He then called three students and asked them to write 3 seven digit numbers, and they wrote 1029854, 9621437, and 7729753. Abhas wrote another three numbers – 8970145, 378562, 2270246 – and asked Elen to add, which he summed up as 35726838. Then, the paper was opened, the entire class was drop-dead silent to see 35726838 on the paper. Just then the bell rang, the children shouted, “Sir, please tell… please tell… how did you do this magic?” Abhas smiled and said, “RAMANUJAN” and left. One of the children said, “Sir knows magic.” Another said, “He can foretell the future!” For the rest of the day, the children’s minds were engrossed in numbers and the fun involved.

Betaal concluded the story here and asked, “O king! Abhas was a simpleton, he didn’t know any magic but how did he know the answers and that too of such large numbers? He should have given some hint to the children, which he didn’t. He just smiled and left. Please answer my questions or else I will behead you.”

The king replied, “Abhas was an intelligent man with extraordinary presentation skills. He presented it so well that the children were spellbound. He did give the hint when he said RAMANUJAN, the great mathematician. The number of letters in RAMANUJAN is 9. He did the magic with the number 9. In the first case when Prakriti wrote 56287, he wrote a 2 in the lakhs place, and subtracted 2* from the unit’s place, so the number became 256285. He kept it a secret. When another child wrote 79286, he wrote 20713, the sum is 99999, which is 100000-1. When the third child wrote 35941, he wrote 64058, the sum again is 99999, which is 100000-1. Now the total sum is 56287 + 100000 – 1 + 100000 – 1 = 256285.

In a simple way he presented this. In the second case, he did the same, but as it was a seven step addition, he wrote 3 in the crore’s place and subtracted 3# from the unit’s place as one number resulted as clue for the answer and another three pairs, each with the value (10000000-1), so he wrote 35726838. For each digit, he wrote another digit so that the sum was 9. For the digit 9, he took 0 and vice versa. With this he made the class more interesting than the games period and instilled a love for mathematics among the children. A great teacher inspires!

Oh! King Vikram, you are brilliant in mathematics too, not only did you clear my doubt but you also enriched me about the subject, but by answering this question you broke your silence!”

Betaal chortled and glided back to the tree.

*Abhas used the number 2 here because he put in two numbers to the five step addition, numbers which when added to the previous numbers written by the students resulted in the magic number 99999 which is 100000-1, therefore for two pairs the sum was 200000-2. Hence, he subtracted 2 from the unit digit of the 5 digit number and wrote a 2 in lakhs place of Prakriti’s number.

#Same logic as previously applied. Since Abhas put in three numbers in the seven step addition, he used the number 3 here.

The author is an enthusiastic educator of mathematics and writes on topics related to innovative and engaging educational methods. He is a CBSE resource person for teacher professional development programmes. He is known for his creative skills, story writing, dramatic and mimicry abilities, disciplined lifestyle and contributions as a community worker. He can be reached at anilpatnaik8@gmail.com.