Aiming and thinking games: kumasha, intembe and igisoro – Rwandan Traditional Games (Senior 4 Physical Education) | Ganzaa

Rwandan Traditional Games

Lessons

Senior 4 · Physical Education

Rwandan Traditional Games

3 lessons

Lesson 2 of 3

Aiming and thinking games: kumasha, intembe and igisoro

25 min

A ring rolling past a line of archers

Imagine young people standing in a row, each with a bow. Someone rolls a ring cut from the stem of a banana plant across in front of them, with a hole in its middle. Each archer tries to send an arrow through the hole while the ring is still moving. This was intembe. Its partner game, kumasha, was a contest of aim at a fixed target, often a banana trunk, and it trained the young for the hunt and for war. Both are games of the eye, the hand and the mind. So is igisoro, Rwanda's ancient board game of counting and planning.

In this lesson you play school versions of the two aiming games with safe objects, measure accuracy with statistics, work out how far ahead of a moving target to aim, and use arithmetic to plan your moves in igisoro.

Definition

Kumasha: a traditional contest of aim in which players shoot or throw at a fixed target, such as a banana trunk.

Intembe: a traditional aiming game in which players shoot at a ring of banana stem rolled past them, trying to pass through its central hole.

Igisoro: a two-player game of the mancala family played on a board of 4 rows of 8 pits with 64 seeds; each player sows seeds around his or her own two rows.

Accuracy: how close throws land to the centre of the target, measured by the mean score. Consistency: how little the scores vary, measured by the range or the standard deviation.

Hit rate: $\frac{\text{number of hits}}{\text{number of throws}} \times 100\%$ .

School kumasha and intembe

Bows, arrows and spears are never used in a school lesson. The skill of aiming is trained just as well with bean bags, tennis balls or soft balls. For kumasha, paint a target with three rings on a board or on a section of banana trunk, worth 3 (centre), 2 and 1 points. For intembe, roll a hula hoop or an old bicycle tyre across the lanes 4 m in front of the throwers; a throw scores when the ball passes through the moving hoop.

Everyone waits behind the waiting line until it is their turn.
Throw only on the teacher's whistle; all players throw, then all players fetch on a second whistle. Nobody enters the safety zone while anyone is holding a ball.
Lanes are at least 3 m apart so that a wild throw cannot hit a neighbour.

Worked example

Worked example 1: accurate or consistent? In a kumasha contest Uwase and Mugisha throw 10 bean bags each at a 3-ring target (3, 2, 1 points; 0 for a miss).

Player	Scores
Uwase	3, 0, 3, 1, 3, 0, 3, 2, 0, 3
Mugisha	2, 2, 1, 2, 2, 1, 2, 2, 2, 1

Means: $\bar{x}_{U} = \frac{18}{10} = 1.8 \qquad \bar{x}_{M} = \frac{17}{10} = 1.7$
Ranges: Uwase $3 - 0 = 3$ ; Mugisha $2 - 1 = 1$ .
Standard deviation, $\sigma = \sqrt{\frac{\sum (x - \bar{x})^{2}}{n}}$ : for Uwase $\sum (x - \bar{x})^{2} = 17.6$ , so $\sigma = \sqrt{1.76} = 1.33$ ; for Mugisha $\sum (x - \bar{x})^{2} = 2.1$ , so $\sigma = \sqrt{0.21} = 0.46$ .
Hit rates: Uwase 7 of 10 = 70%; Mugisha 10 of 10 = 100%.

Interpretation. Uwase is slightly more accurate on average and often hits the centre, but she misses three times: she is far less consistent. Mugisha never misses but rarely hits the centre. Uwase should work on a repeatable throwing action; Mugisha on aiming at the centre rather than "somewhere on the board". In a team contest where every miss costs, Mugisha is the safer choice.

Worked example

Worked example 2: aiming ahead of a moving hoop. In school intembe, the hoop rolls across at $2.0\,\mathrm{m\,s^{-1}}$ . Ishimwe throws from 4.0 m away, and her ball travels at about $8.0\,\mathrm{m\,s^{-1}}$ . Where should she aim?

Time for the ball to reach the hoop's path: $t = \frac{4.0\,\mathrm{m}}{8.0\,\mathrm{m\,s^{-1}}} = 0.50\,\mathrm{s}$
Distance the hoop rolls in that time: $d = 2.0 \times 0.50 = 1.0\,\mathrm{m}$

She must throw at a point about 1 m ahead of the hoop, not at the hoop itself. This is called leading the target, and it is the same skill a footballer uses when passing into a team-mate's run. The archers of intembe had to judge it by eye.

Igisoro: counting before you touch

In Senior 1 you learned to sow, to relay-sow and to capture, numbering your 16 pits 1 to 8 along the back row and 9 to 16 along the front row, anticlockwise. You also learned the rule "add the seeds to the pit number; if the answer is more than 16, subtract 16". Written with the modulo operation (the remainder after division), the pit $\ell$ where your last seed lands, sowing $n$ seeds from pit $p$ (for $n < 16$ ), is

\ell = \big( (p + n - 1) \bmod 16 \big) + 1

A strong player works this out for every pit before touching a seed, then checks each landing pit: is it occupied (so the turn continues)? is it in the front row, facing two of the opponent's pits that both hold seeds (so a capture is possible)?

Worked example

Worked example 3: choosing the best move. In the position in the diagram, Player A considers three moves: pit 3 (6 seeds), pit 7 (5 seeds) and pit 14 (5 seeds).

Move	Landing pit	What happens
Pit 3, 6 seeds	$(3 + 6 - 1) \bmod 16 + 1 = 9$	Pit 9 held 2 seeds, so it is occupied; it is in the front row, and B's two pits opposite hold 3 and 4. Capture 7 seeds, sown again from pit 3 into pits 4 to 10
Pit 7, 5 seeds	$(7 + 5 - 1) \bmod 16 + 1 = 12$	Pit 12 was empty: the turn ends at once
Pit 14, 5 seeds	$(14 + 5 - 1) \bmod 16 + 1 = 3$	Pit 3 held 6 seeds: relay-sow its 7 seeds from pit 4; the last lands in pit 10, which is empty, so the turn ends. No capture: pit 3 is in the back row

Decision. Pit 3 wins 7 seeds; the other two win nothing. Notice also B's mistake: B left seeds in both pits of column 8. Keeping a front pit empty protects the back pit behind it.

Video: "Igisoro: The traditional board game in Rwanda", Trans World Sport. Watch how fast experienced players sow, and how they count the seeds in a pit before they pick them up.

Tip

Two habits of good aimers and good igisoro players. Aim at where the target will be, not where it is. Count where your last seed will land before you touch a pit.

Warning

Common mistakes. Fetching a ball before the second whistle. Standing in the safety zone "just to watch". Judging a thrower only by her best throw: use the mean and the spread. In igisoro, forgetting that the pit you start from is emptied, and moving before checking whether the opponent can capture next turn.

✦

Practice

Describe the traditional games kumasha and intembe, and explain why the school versions use balls or bean bags.
Give three safety rules for a school throwing range and the danger each one prevents.
Scores in 8 throws: 3, 2, 3, 0, 2, 3, 1, 2. Calculate the mean, the range and the hit rate.
A hoop rolls at 1.5 m s⁻¹. A ball thrown from 5.0 m travels at 10 m s⁻¹. How far ahead of the hoop should the thrower aim?
Using $\ell = ((p + n - 1) \bmod 16) + 1$ , find the landing pit for: (a) pit 5 with 8 seeds; (b) pit 13 with 7 seeds.
In Worked example 3, explain why the move from pit 7 is the weakest.
Player B wants to protect the 4 seeds in the back pit of a column. What should B do with the front pit of that column, and why?
Evaluate whether igisoro belongs in Physical Education even though it is not physically demanding.

Show answersHide answers

Kumasha: a contest of aim at a fixed target such as a banana trunk. Intembe: shooting through the hole of a banana-stem ring rolled past the players. Bows, arrows and spears could kill or blind; balls and bean bags train the same aiming skill safely.
For example: a waiting line (stops pupils walking into the throwing area); throw and fetch only on whistles (no one is downrange during a throw); lanes 3 m apart (a wild throw cannot hit a neighbour); a safety zone behind the targets (no one stands where missed throws land).
Sum = 16, mean = 16 ÷ 8 = 2.0; range = 3 − 0 = 3; hits 7 of 8 = 87.5%.
t = 5.0 ÷ 10 = 0.50 s; d = 1.5 × 0.50 = 0.75 m ahead.
(a) (5 + 8 − 1) mod 16 + 1 = 12 + 1 = 13. (b) (13 + 7 − 1) mod 16 + 1 = 19 mod 16 + 1 = 3 + 1 = 4.
Its last seed lands in pit 12, which is empty, so the turn ends at once: no relay and no capture, and it moves five seeds forward for nothing.
Keep that front pit empty: a capture needs seeds in both the front and the back pit of the column, so the back pit cannot be taken.
Yes: PE also develops concentration, planning, patience, fair play and respect for an opponent; igisoro is part of Rwanda's sporting culture; and it suits pupils who cannot do hard exercise, so it is inclusive. It does not replace physical activity, so it complements rather than replaces active games.

Quick check

Remember

Kumasha (fixed target) and intembe (rolling target) train aim; at school use balls or bean bags, a waiting line, whistles and a safety zone.
Mean = accuracy; range and standard deviation = consistency; hit rate = hits ÷ throws × 100%.
Lead a moving target by distance = target speed × flight time.
Igisoro: last pit $\ell = ((p + n - 1) \bmod 16) + 1$ ; capture only from an occupied front pit facing two occupied pits.

Sources and credits

Imikino gakondo mu Rwanda, Wikipedia contributors, Kinyarwanda Wikipedia, licensed under CC BY-SA 4.0: the descriptions of kumasha and intembe. Translated from Kinyarwanda and adapted by Ganzaa.
Igisoro, Wikipedia contributors, Wikipedia, licensed under CC BY-SA 4.0: the board, the seeds, anticlockwise sowing, relay sowing and the capture rule. Adapted by Ganzaa.
Photo: Rwandan old Man playing Igisoro with kids around, Davyimage, Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: "Igisoro: The traditional board game in Rwanda", Trans World Sport, embedded from YouTube.
School rules, range and board diagrams, worked examples, practice and quick check: written by Ganzaa. The scores and the board position are illustrative.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1A ring rolling past a line of archers

2School kumasha and intembe

3Igisoro: counting before you touch

A ring rolling past a line of archers

School kumasha and intembe

Igisoro: counting before you touch