Memory Challenge - Working Memory Test

Memory Challenge - Working Memory Test

Study the following picture which includes 20 items for 2 minutes; you should remember what are included in it!

Memory Challenge - Working Memory Test

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Now, take a pen and paper, try to remember what are included in the above illustration, and write them (names) on the paper. You have 2 minutes to remember!

Memory Challenge - Visual Test

Memory Challenge - Visual Test

For one minute (60 seconds), study the following picture where 7 letters are connected by 10 lines:

Figure 1 - Memory Challenge - Visual Test

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The following is a copy of the above picture but one line is missing. You should remember what two letters were connected by that line.

Figure 2 - Memory Challenge - Visual Test

Memory Challenge - Visual String Study

Memory Challenge - Visual String Study

Study the following figure for 2 minutes and then answer the questions that follow:

Memory Challenge - Visual String Study

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Questions:

1. Which of the following letters is not depicted in the figure?

a) H
b) V
c) Y
d) Q

2. Which string of letters is located inside the central circle?

a) BGHF
b) CARW
c) FGHB
d) CRAW

3. Which of the following letters is not depicted in the circle located at the left of the central circle?

a) U
b) V
c) O
d) Q

Equivalent to the original rotated in three dimensions!

Which of A or B is equivalent to the original block rotated in three dimensions?

source: Brain Flexing IQ Tests by Fraser Simpson.

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Answer:

A

Piles with Pebbles

You are given three piles with 5, 49 and 51 pebbles respectively. Two operations are allowed: (a) merge two piles together or (b) divide a pile with an even number of pebbles into two equal piles. Is there a sequence of operations that would result in 105 piles with one pebble each?

source: From a compendium of Math competition problems.

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Answer:


Since all three piles are odd, the first operation must be merger of two existing piles, resulting in an even-sized pile and an odd-sized pile. Let g denote the greatest common divisor of these two pile sizes. Since one pile is odd sized and the other pile is even sized, g must be odd. For odd g, no matter what sequence of operations is carried out (merger of two existing piles or division of an even pile into two equal piles), every pile size will continue to be a multiple of g. If g > 1, then we can never reach a configuration where all piles are size 1. Now, starting with {5, 49, 51}, three states are possible: {54, 51}, {5, 100} and {49, 56}. The GCD is 3, 5 and 7, respectively, in these three states. So we can never get 105 piles with 1 pebble each.