# digits

In this edition of ‘Adventures’ we study a few miscellaneous problems, mostly from the Pre-Regional Mathematics Olympiad (PRMO; this year’s PRMO was conducted on August 19 in centres all over the country). As usual, we pose the problems first and present solutions later.

## Divisibility by 7

This article deals with a simple test for divisibility by 7 for natural numbers having a minimum of four digits. Here, a case of a six-digit number is proved initially and similar proofs follow for other higher-digit numbers.

## Sums of Consecutive Natural Numbers

Swati Sircar and Sneha Titus, writing on the Sums of Consecutive Natural Numbers, show how mental mathematics becomes visual all of a sudden, and this Low Floor High Ceiling activity is sure to appeal to a variety of learning styles.

## 153, and so on and on and on …

On the AtRiUM FaceBook page we came across this striking set of arithmetical relations (posted by a reader, Ms Paromita Roy). We leave the verification and proof to the reader.

## Divisibility Tests by Powers of 2

There is a well-known test for divisibility by powers of 2: to check the divisibility of a number M by 2n, we form a new number M' using only the last n digits of M and then examine the divisibility of that number (i.e., M') by 2n. The test works because of the easily-proved fact that M is divisible by 2 if and only if M' is divisible by 2n.

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